Groups with certain thickness have empty Floyd boundary.
problem Understanding Floyd boundaries of groups.
method Proving triviality of Floyd boundaries for thick groups.
result Trivial Floyd boundary for thick groups.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “Floyd boundary”
For finitely supported random walks on finitely generated groups we prove that the identity map on extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This yields new results for relatively hyperbolic groups. Our key e…
The paper consists of two parts. In the first one we show that a relatively hyperbolic group splits as a star graph of groups whose central vertex group is finitely generated and the other vertex groups are maximal parabolic subgroups. As a corollary we obtain that every group which admits 3-discontinuous and 2-coc…
In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the growth rate of the group. In the proof, we study a special class of conical points …
We introduce the notion of controlled Floyd separation between geodesic rays starting at the identity in a finitely generated group G. Two such geodesic rays are said to be Floyd separated with respect to quasigeodesics if the (Floyd) length of c-quasigeodesics (for fixed but arbitrary c) joining points on the geodesic…
Classifies nonorientable surfaces in a specific type of bundle.
problem Classifying surfaces in a specific type of bundle.
method Uses ideas from Floyd, Hatcher, and Thurston; puts surface in 'Morse position' with respect to the bundle projection.
result Classifies incompressible, boundary-incompressible, nonorientable surfaces.
Computes genus of specific knots using Floyd and Hatcher's tools.
problem Computing the genus of satellite tunnel number one knots and torti-rational knots.
method Uses Floyd and Hatcher's tools and an algorithm to compute genus and slopes of minimal genus Seifert surfaces.
result Computes genus and slopes for specific knots.
In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known results on limit sets of geometrically finite Kleinian groups are derived in general…
Adapts Floyd-Warshall algorithm for RL to improve multi-goal task learning.
problem Limited transfer of learned information in model-free RL for dynamic goal tasks.
method Adapts Floyd-Warshall algorithm for RL to learn goal-conditioned action-value functions.
result FWRL achieves higher reward strategies in multi-goal tasks with fewer samples.
The Martin boundary of certain groups is stable under specific conditions.
problem Stability of Martin boundaries in relatively hyperbolic groups.
method Extending Floyd-Ancona inequalities, defining spectral degenerescence, and proving stability criteria.
result The Martin boundary of admissible symmetric finitely supported probability measures on geometrically finite Kleinian groups of dimension at most 5 is always strongly stable.
The paper develops a theory of conformal density at infinity for groups with contracting elements.
problem Understanding conformal dynamics at infinity for groups with contracting elements.
method Introducing a class of convergence boundary and establishing the basic theory of conformal density on it.
result Unified theory of conformal density on various boundaries for different types of groups.
We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the SL_2(C) character variety of a surface, one associated to complex projective structures and the other associated to a 3-manifold. Using the Morgan-Shalen compactification of the cha…
Cannon, Floyd and Parry have studied the modulus of finite subdivision rules extensively. We investigate the properties of the modulus of subdivision rules with linear and exponential growth at every vertex, using barycentric subdivision and a subdivision rule for the Borromean rings as examples. We show that the subdi…
Culler and Shalen, and later Yoshida, give ways to construct incompressible surfaces in 3-manifolds from ideal points of the character and deformation varieties, respectively. We work in the case of hyperbolic punctured torus bundles, for which the incompressible surfaces were classified by Floyd and Hatcher. We conver…
We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often efficient and natural…
We obtain general formulae expressing Hirzebruch genera of a manifold with Z/p-action in terms of invariants of this action (the sets of weights of fixed points). As an illustration, we consider numerous particular cases of well-known genera, in particular, the elliptic genus. We also describe the connection with the s…
Generalizes theorem for topological -manifolds with linear Lie groups .
problem Understanding topological -manifolds with linear Lie groups .
method Using countable CW complexes and Palais-proper actions.
result Topological -manifolds have -homotopy type of countable -CW complexes.
In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure and that is invariant under a certain involution is the ideal triangulation defin…
The paper combines several fortunate mini miracles to achieve its two objectives. These were woven together in a several year's effort to answer a question raised by Iz Singer a decade ago. Our answer is accessible to the topologist, to the differential geometer and to the analyst who appreciates the statement of the I…
Cannon, Floyd, and Parry have studied subdivisions of the 2-sphere extensively, especially those corresponding to 3-manifolds, in an attempt to prove Cannon's conjecture. There has been a recent interest in generalizing some of their tools, such as extremal length, to higher dimensions. We define finite subdivision rul…
Kawakubo and Uchida showed that, if a closed oriented -dimensional manifold admits a semi-free circle action such that the dimension of the fixed point set is less than , then the signature of vanishes. In this note, by using -signature theorem and the rigidity of the signature operator, we generaliz…
The paper explores growth rates and Perron numbers in Coxeter systems with low-dimensional Davis complexes.
problem Investigating growth rates and specific types of numbers in Coxeter systems with Davis complexes of low dimension.
method Examining Coxeter systems with Davis complexes of dimension at most 2, focusing on growth rates and specific types of numbers.
result The growth rate of Coxeter systems with Davis complexes of dimension at most 2 are either Salem or Pisot numbers, depending on the Euler characteristic.
Invariants for colored links found, with topological protection of certain knots.
problem Finding invariants for colored links and understanding their topological stability.
method Equivariant bordism groups of Conner and Floyd, topological surgeries.
result Topological protection of certain tricolored knots, with specific transformations.
Proves minimal growth rate for Coxeter groups in hyperbolic space.
problem Finding minimal growth rate Coxeter groups in hyperbolic space.
method Generalizes methods from cocompact case to non-cocompact groups.
result Proves minimal growth rate for Coxeter groups .
We simplify Thurston norm computation for 2-bridge link complements.
problem Understanding the complexity of Thurston norm unit balls in 3-manifolds.
method Utilized Floyd and Hatcher's surface description and integral class minimization.
result Thurston norm unit balls of 2-bridge link complements have at most 8 faces.
M/F-Theory as Mf-Theoryhep-th
New mathematical framework connects M-theory charges to stable homotopy groups.
problem Quantization of fluxes in M-theory and their mathematical representation.
method Establishing a correspondence between M-theory phenomena and stable homotopy theory concepts.
result Found a direct link between M-theory charges and stable homotopy groups.
Develops parametrised Poincaré duality for equivariant fixed points.
problem Understanding equivariant fixed points in non-presentable settings.
method Introduces parametrised Poincaré duality in parametrised higher category theory, proving basechange results.
result Generalises Cnossen's twisted ambidexterity to non-presentable settings and applies to isotropy separation methods.
Paper details Hilbert-curve for high-performance data mining.
problem Efficiently mapping multi-dimensional data to one dimension.
method Defines Hilbert-curve using finite automaton and context-free grammar.
result Cache-oblivious algorithms for matrix operations and clustering.
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.
Proves equivalence of two types of boundaries in metric spaces.
problem Proving equivalence of two types of boundaries in metric spaces.
method Analyzes and compares contracting and -Morse boundaries.
result Proves equivalence of 1-Morse boundary and contracting boundary as topological spaces.
Study boundary value problems for elliptic operators on manifolds.
problem Characterize and analyze boundary conditions for first-order elliptic differential operators.
method Develops a new framework for elliptic boundary conditions, proving equivalence and regularity of solutions.
result Elliptic boundary conditions yield a Fredholm operator on compact manifolds.
Proves unique extension of Bartnik boundary data for stationary vacuum spacetimes.
problem Unique extension of Bartnik boundary data for stationary vacuum spacetimes.
method Elliptic boundary value problem for stationary vacuum equations combined with Bartnik boundary conditions.
result Bartnik boundary data near standard flat data admits a unique stationary vacuum extension locally.
Study defines a new boundary for CAT(0) groups, invariant under quasi-isometries.
problem Defining boundaries for CAT(0) groups when visual boundaries are not well-defined.
method Introducing a sublinear function κ to define κ-Morse boundaries, showing invariance under quasi-isometries.
result κ-Morse boundaries are invariant and metrizable for CAT(0) groups.
Proves well-posedness for Einstein equations with specific boundary conditions.
problem Well-posedness of vacuum Einstein equations with twisted Dirichlet boundary conditions.
method Proves local-in-time well-posedness for the IBVP of the Einstein equations with specified conformal class and scalar densities.
result Proves well-posedness for the Einstein equations with twisted Dirichlet boundary conditions.
We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both second-order and fourth-order symplectic Laplacians and establish Hodge theories for the …
Abstracts a construction of boundary triplets for self-adjoint elliptic problems.
problem Computing the index of families of self-adjoint elliptic boundary problems.
method Abstract axiomatic version of boundary triplets and their applications.
result Analytic proof of index theorem and computation of index differences.
Study shows boundary curves of free boundary minimal surfaces are circles.
problem Characterizing boundary curves of free boundary minimal surfaces.
method Holomorphic techniques applied to the unit ball in Euclidean 3-space.
result Intersection curves of free boundary minimal surfaces with the unit sphere are all circles.
The paper studies Ricci flow on manifolds with boundary, proving existence, uniqueness, and boundary conditions preservation.
problem Ricci flow on manifolds with boundary.
method Proving short-time existence and uniqueness of the solution, and showing boundary conditions preservation.
result The flow preserves natural boundary conditions under certain curvature conditions.
Unique compact Fuchsian manifolds with convex boundary are determined by their boundary.
problem Identifying compact Fuchsian manifolds with convex boundaries.
method Proving uniqueness based on the induced path metric on the boundary.
result Compact Fuchsian manifolds with convex boundaries are uniquely determined by the induced path metric on the boundary.
Generalizes Bestvina's -boundaries to coarse -boundaries.
problem Establishing properties of -boundaries for groups.
method Introducing a new concept of a 'coarse -boundary' and proving theorems about it.
result Admitting a coarse -boundary is a pure quasi-isometry invariant.
We introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with rays that identify the "hyperbolic directions" in that space. This boundary is a quasi-isometry invariant and thus produces a well-defined boundary for any finitely generated group. In the case of a prope…
Study on quasi-Einstein manifolds with boundary estimates and inequalities.
problem Understanding the geometry of compact quasi-Einstein manifolds with boundary.
method Sharp boundary estimates and characterization theorems for quasi-Einstein manifolds.
result New geometric inequalities and boundary estimates for quasi-Einstein manifolds.
Proof of local well-posedness for a specific boundary condition in general relativity.
problem Initial boundary value problem in general relativity with umbilic boundary condition.
method Wave coordinates and key observation of momentum constraint validity for umbilic boundaries.
result Local well-posedness established for the initial boundary value problem.
Foundations for free boundary Brakke flows established.
problem Analyzing free boundary flows through singularities
method Introducing unit-regular and cyclic free boundary flows, proving avoidance principle, and introducing inner and outer flows.
result General tools for analyzing free boundary flows through singularities.
Embedded surfaces in a ball have any genus and connected boundary.
problem Existence of embedded free boundary minimal surfaces with specific properties.
method Min-max techniques applied to the unit ball in .
result Existence of embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
Study finds rigid properties of boundary-free hypersurfaces in specific data sets.
problem Rigidity of free boundary hypersurfaces in initial data sets with boundary.
method Extending local splitting theorems and applying results on free boundary MOTS.
result Rigidity results for compact free boundary hypersurfaces in initial data sets with boundary.
The paper studies -stability of surfaces with boundary and derives area estimates.
problem Investigating -stability of surfaces with boundary.
method Analyzing geometric properties and deriving area estimates.
result Derives area estimates and determines the topology of the surface.
The paper shows how sublinearly Morse boundaries can be understood through combinatorial methods.
problem Understanding sublinearly Morse boundaries in cubulated groups and CAT(0) cube complexes.
method Combining geometric and combinatorial approaches to analyze sublinearly Morse boundaries.
result Sublinearly Morse boundaries can be described combinatorially and continuously related to Gromov and Roller boundaries.