In this paper we show that the existence of a non-parabolic local cut point in the Bowditch boundary of a relatively hyperbolic group implies that splits over a -ended subgroup. This theorem generalizes a theorem of Bowditch from the setting of hyperbolic groups to relat…
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48 results for “relative ends theorem”
The Kropholler Conjecturemath.GR
Corrects a flawed proof of the Kropholler Conjecture.
problem Kropholler Conjecture in relative group theory.
method Explains the flaws and proposes possible ways to correct the proof.
result Provides a clearer understanding of the conjecture's proof difficulties.
Ends and end cohomologymath.AT
Ends and cohomology theory for noncompact spaces.
problem Study of noncompact spaces and their invariants.
method Exposition of ends theory, introduction of reduced end cohomology, proof of theorems.
result Proof of a theorem on end cohomology of end sums of manifolds.
Almost Invariant Setsmath.GR
A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives information about the structure of the Sageev cubing.
Groups with semistable peripheral subgroups are semistable.
problem Semistability of fundamental groups in relatively hyperbolic groups.
method Generalization of semistability from 1-ended subgroups to finitely generated subgroups with semistable fundamental groups.
result Semistability of fundamental groups in more general relatively hyperbolic groups.
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This gives a relative version of Stallings' Theorem on the structure of groups with mo…
We generalise the Karrass-Pietrowski-Solitar and the Nielsen realisation theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel--Mosher and on the outer space of a fr…
We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…
Clarifies boundary criterion for non-one-ended subgroups in cubulation theory.
problem Boundary criterion for relative cubulation in non-one-ended subgroups.
method Showed that if boundary criterion is satisfied for a relatively hyperbolic group, the group admits a relatively geometric action on a CAT(0) cube complex.
result The refinement of the boundary criterion is useful for constructing new relative cubulations.
In this paper we study the relative Chow and -stability of toric manifolds in the toric sense. First, we give a criterion for relative -stability and instability of toric Fano manifolds in the toric sense. The reduction of relative Chow stability on toric manifolds will be investigated using the Hibert-Mumford cr…
On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifoldsmath.DG
We show that the periodic -invariants introduced by Mrowka--Ruberman--Saveliev~\cite{MRS3} provide obstructions to the existence of cobordisms with positive scalar curvature metrics between manifolds of dimensions and . The proof combines a relative version of the Schoen--Yau minimal surface technique with an…
We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact manifold without boundary the holonomies of properly convex structures form an …
Accessible groups with infinitely many ends have infinitely many twisted conjugacy classes.
problem Characterizing groups with infinitely many ends and their conjugacy classes.
method Analyzing accessible groups and relatively hyperbolic groups to deduce properties.
result Groups with infinitely many ends have infinitely many twisted conjugacy classes.
Characterizes ends and coends of graph pairs using quasi-median graphs.
problem Understanding the number of ends and coends in graph pairs.
method Characterizes ends and coends using quasi-median graphs.
result Characterizes ends and coends of graph pairs in terms of quasi-median graphs.
Uniform K-homology theory applied to elliptic operators on manifolds with boundary.
problem Developing a theory to study boundary conditions for elliptic operators on non-compact manifolds.
method Theory of relative uniform K-homology, developing a relative index map.
result Uniform K-homology classes of boundary conditions and their connection to the higher ρ-invariant.
Study of non-metrizable manifolds' ends, generalizing Nyikos's theorem.
problem Characterizing non-metrizable surfaces with ends.
method Introducing short and long ends, developing theory of spaces of ends.
result Characterization of surfaces as metrizable manifolds plus long pipes.
Regularization is important for end-to-end speech models, since the models are highly flexible and easy to overfit. Data augmentation and dropout has been important for improving end-to-end models in other domains. However, they are relatively under explored for end-to-end speech models. Therefore, we investigate the e…
Locally connected boundaries proven for relatively hyperbolic groups.
problem Proving local connectedness of boundaries for relatively hyperbolic groups.
method Using a group pair that is relatively one ended, and removing restrictions on cardinality and peripheral subgroups.
result The Bowditch boundary of is locally connected.
Extends a theorem for first-order elliptic operators on manifolds.
problem Proving the relative index theorem for general first-order elliptic operators.
method Using boundary value problems and graphical decomposition of elliptically regular boundary conditions.
result Proves the relative index theorem for general first-order elliptic operators.
A new comparison theorem for geometric spaces.
problem Geometric space comparison theorems.
method Relative form of Toponogov comparison theorem.
result New geometric space comparison theorem established.
Proves Farrell--Jones Conjecture for hyperbolic groups and their automorphisms.
problem Proving the Farrell--Jones Conjecture for automorphisms of hyperbolic groups.
method Analyzes JSJ decompositions and applies results to automorphisms of hyperbolic groups.
result Proves the fibred Farrell--Jones Conjecture for a class of relatively hyperbolic groups.
Proves mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with various ends.
method Quantitative analysis of scalar curvature on manifolds with arbitrary ends.
result Proves the positive mass theorem for a wide class of manifolds.
Researchers prove positive mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with non-compact ends.
method Developed techniques to handle non-compact singular sets and used metrics.
result Established positive mass theorem for arbitrary ends with metrics.
Proves positive mass theorem for specific manifold types.
problem Positive mass theorem for manifolds with arbitrary ends.
method Proof for asymptotically flat and Euclidean manifolds.
result Validates positive mass theorem in new manifold types.
DRSVM uses deep learning to rank relative attributes between image pairs.
problem Classifying relative attributes between image pairs.
method Deep Siamese network with rank SVM loss function.
result DRSVM outperforms state-of-the-art methods on multiple datasets.
We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Com…
In this paper, we extend Roe's cyclic -cocycle to relative settings. We also prove two relative index theorems for partitioned manifolds by using its cyclic cocycle, which are generalizations of index theorems on partitioned manifolds. One of these theorems is a variant of [M. Karami-A.H.S. Sadegh-M.E. Zadeh, arXiv:…
New positive mass theorems for ALH manifolds with toroidal ends.
problem Proving positive mass theorems for asymptotically locally hyperbolic manifolds.
method Utilizes properties of marginally outer trapped surfaces and a new technique involving μ-bubbles.
result Obtained new positive mass theorems for asymptotically locally hyperbolic manifolds without boundary.
We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes' Fredholm theory for general end-periodic operators. Our index theorem is expressed in t…
The paper proves density and positive mass theorems for incomplete manifolds.
problem Proving density and positive mass theorems for manifolds with incomplete ends.
method Using harmonic asymptotics and quantitative positive mass theorem improvements.
result Improved quantitative positive mass theorem in dimensions 3 to 7.
The paper defines capacities for minimal graphs over manifolds and proves the half-space property.
problem Characterizing minimal graphs and their properties over manifolds.
method Defining capacities using relative volume, studying solutions of bounded variation, and analyzing boundary behavior.
result Proves the half-space property for -parabolic manifolds.
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
New proof of splitting theorem and finite ends of minimal hypersurfaces in nonnegative curvature manifolds.
problem Proving splitting theorem and finite ends of minimal hypersurfaces in nonnegative curvature manifolds.
method New proof of splitting theorem and construction of weighted minimizing geodesics at infinity.
result Minimal hypersurfaces with finite index in manifolds with nonnegative biRic curvature must have finite ends.
Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shieldsmath.DG
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
The controlled end and h-cobrodism theorems (Ends of maps I, 1979) are used to give quick proofs of the Top/PL and PL/DIFF product structure theorems.
Homotopy momentum map extends Noether's theorem in general relativity.
problem Extending Noether's theorem to spacetime vector fields.
method Using homotopy momentum map and -algebras.
result Extension of conserved currents to spacetime vector fields.
Defines new Roe algebras for cylindrical spaces, solving metric curvature problems.
problem Existence and classification of metrics with positive scalar curvature on spaces with cylindrical ends.
method Variant of Roe algebras for cylindrical spaces, relating to relative higher index theory.
result Defines higher rho-invariants and provides a concise proof of a related result.
Extends Gromov's theorem with amenable covers.
problem Gromov's Vanishing Theorem limitations.
method Gromov's multicomplex theory, relative bounded cohomology.
result Relative version of Gromov's Vanishing Theorem.
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.
On relative normal modesmath.SG
We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative perodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular we prove that under appropriate hypothes…
The paper explores curvature-free effects in manifolds with volume growth and ends-counting.
problem Investigating curvature-free effects in manifolds with volume growth and ends-counting.
method Establishing two main theorems about volume growth and ends-counting.
result Proves the existence of smooth bounded mean-concave exhaustion and escaping geodesic lines.
Study the positive mass theorem for certain asymptotic manifolds.
problem Positive mass theorem for specific types of asymptotic manifolds.
method Compactification and analysis of Riemannian manifolds.
result Established conditions for the positive mass theorem.
Extends ASD connection existence to 4-manifolds with cylindrical ends.
problem Existence of ASD connections on 4-manifolds with specific ends.
method Extends gluing theorems to cylindrical ends, using mASD connections.
result Establishes existence of ASD connections on 4-manifolds with cylindrical ends.
Proves positive mass theorem for hyperbolic manifolds with ends.
problem Establishing positive mass theorem for complex initial data sets.
method Used spectral PSC, Jang equation, and quantitative shielding theorem.
result Proved positive mass theorem for asymptotically hyperbolic manifolds.
Abstract: Proves relative versions of group splitting results.
problem Group splittings and invariant sets.
method Relative versions of earlier results about almost invariant sets and splittings of groups.
result Existence and uniqueness of relative versions of algebraic regular neighbourhoods and JSJ decompositions.
Foliation of area-minimizing hypersurfaces in asymptotically flat manifolds of higher dimensionmath.DG
The paper proves the existence of area-minimizing hypersurfaces in AF manifolds of higher dimensions.
problem Existence of area-minimizing hypersurfaces in AF manifolds with arbitrary dimension and ends.
method Positive mass theorem for AF manifolds with arbitrary ends and global behavior for hypersurfaces in AF manifolds of dimension ≤ 8.
result Existence and behavior of area-minimizing hypersurfaces in AF manifolds of higher dimensions.
Study generalizes non-interaction theorems for relativistic systems.
problem Understanding interactions in relativistic and non-relativistic systems.
method Generalizes non-interaction theorems for Lorentz violating systems and Galilei invariant systems.
result Extends analysis to very special relativity and anisotropic systems.