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.
Geometric group theory explores groups through their geometric properties.
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties and invariants of groups invariant under quasiisometry, rigidity, hyperbolic spa…
Invites geometers to Garside theory for mapping class groups.
Survey on non-positively curved cube complexes and geometric group theory.
Study algebraic K-theory of 3-manifold groups using Farrell-Jones isomorphism and geometrization.
Simplified Milnor-Schwarz lemma for geometric group theory.
New theory connects geometry without relying on connections.
We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering matrices and their functional equations.
Extends potential theory to Carnot groups, estimating Hausdorff dimension.
Proves conjecture for hyperbolic-by-cyclic groups using geometric methods.
Geometric techniques reveal new insights into Gromov-Witten invariants.
Surveying connections between graph combinatorics and algebraic right-angled Artin groups.
The paper proposes conjectures about moduli space rigidity.
Survey discusses new ideas in geometric group theory and their applications.
Survey of combination theorems in geometry and dynamics.
We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Ch…
Surveying Hitchin representations of Fuchsian groups.
Survey on handlebody groups and their properties.
Study on mappings in Carnot groups, proving rigidity results.
Action of loop groups on Cuntz algebras constructs geometric twists.
Equivalence proven between equivariant K-theory and K-homology for certain matrix group actions.
The book explores Lie groups and Carnot-Carathéodory spaces, highlighting their applications in metric geometry and geometric group theory.
Develops theory of relatively geometric actions on CAT(0) cube complexes.
Investigates connections in Lie group bundles, focusing on geometric reduction.
New findings link 3D shapes to group properties.
Develops Patterson-Sullivan theory for coarse cocycles.
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of easy groups. As we will explain, these properties are central in the theory of d…
Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The definition of geometric Wall groups involves homology with local coefficients a…
This paper extends geometric structure theory to infinite type structures.
We extend several techniques and theorems from geometric group theory so that they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). A second way that we generalize earlier results is by eliminating freeness requirements often placed on the group actions. In doing so, we allow for groups wi…
We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion of the parametrization by topological data of the components of the closure of …
These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in Representation Theory such as the group algebra of a Weyl group, the universal …
We study meromorphic actions of unipotent complex Lie groups on compact Kähler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable Kähler structures obtained by symplectic reduct…
Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.
Study of circle configurations in the plane, proving aspherical space and computing fundamental groups.
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly disconnected). We characterise the subsurfaces which lead to virtually abelian ge…
Let G be a discrete group and let X be a G-finite, proper G-CW-complex. We prove that Kasparov's equivariant K-homology groups KK^G(C_0(X),\C) are isomorphic to the geometric equivariant K-homology groups of X that are obtained by making the geometric K-homology theory of Baum and Douglas equivariant in the natural way…
GQML uses symmetries from representation theory to improve quantum machine learning.
New method proves length spectrum rigidity in various geometric settings.
We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator, canonically associated, via the so-called clutching map. To this end we adapt to our fra…
This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.
We inspect Vietoris-Rips complexes of certain metric spaces using a new generalization of Bestvina-Brady discrete Morse theory. Our main result is a pair of metric criteria on , called the Morse Criterion and Link Criterion, that allow us to deduce information about the homotopy types of certain $VR_t(…
Characterizes Coxeter groups with convex cocompact representations in projective space.
This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often contractible, so distinguishing one from another requires techniques beyond the standard …
A finitely presented group is semistable at infinity if all proper rays in the Cayley 2-complex are properly homotopic. A long standing open question asks whether all finitely presented groups are semistable at infinity. This article provides a brief introduction to the notion of semistability at infinity in geometric …
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "offici…
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this homology theory with one term and two term (rack) homology theori…