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.
Survey on algebraic K- and L-theory conjecture.
Invites geometers to Garside theory for mapping class groups.
Study algebraic K-theory for specific groups of non-orientable surfaces.
In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-gr…
Uniform interpretation of group theory in manifold homeomorphisms.
Gauge theory for families helps compare 4-manifold groups.
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…
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
Geometric group theory explores groups through their geometric properties.
We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce the conjecture in pseudoisotopy theory for these groups. Finally in B of Theorem 1…
Study on totally symmetric sets with group applications.
Study algebraic K-theory of 3-manifold groups using Farrell-Jones isomorphism and geometrization.
Simplified Milnor-Schwarz lemma for geometric group theory.
Let be a word hyperbolic group. We prove that the algebraic -theory groups of $\dbZ [G]$, $K_n(\dbZ[G])$, have finite rank for all $n\in \dbZ$. For a few classes of groups, we give explicit formulas for the ranks of the algebraic -theory groups of their group rings.
Surveying connections between graph combinatorics and algebraic right-angled Artin groups.
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and Lie groups in that their second groups classify extensions. We use this fact to…
In this paper we define and develop the theory of the cohomology of a profinite group relative to a collection of closed subgroups. Having made the relevant definitions we establish a robust theory of cup products and use this theory to define profinite Poincaré duality pairs. We use the theory of groups acting on prof…
We develop new algebraic methods refining the Witt group of linking forms and Ranicki's torsion algebraic L-groups into double Witt groups and double L-groups. At each prime ideal of the underlying ring, our double Witt groups capture infinitely many more integral signatures of the linking form than the single Witt gro…
Lecture notes on Lie groups and Chern-Simons theory for grad students.
Survey of gauge theory for families of 4-manifolds.
We give formulas for the Whitehead groups and the rational -theory groups of the (integer group ring of the) Hilbert modular group in terms of its maximal finite subgroups.
The paper explores mapping class groups and their quantum field theory representations.
The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.
Tree-graded spaces are generalizations of R-trees. They appear as asymptotic cones of groups (when the cones have cut points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying embeddings of a group into another group, etc. lead to actions of groups on the asy…
The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and an arbitrar…
The book explores analytic properties of groups and their actions.
Develops Johnson-Morita theory for 3D handlebody groups.
We give a survey of the theory of surface braid groups and the lower algebraic K-theory of their group rings. We recall several definitions and describe various properties of surface braid groups, such as the existence of torsion, orderability, linearity, and their relation both with mapping class groups and with the h…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible simple objects. This paper gives a detailed exploration of "topological quantum …
In Classical Knot Theory and in the new Theory of Quantum Invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this note, several classical problems concerning unknotting moves. Our approach uses a new concept, Burnside groups of links, which establishes unexpected re…
This paper approximates SU(2) Chern-Simons theory using finite group gauge theories.
New approach simplifies gauge field theory without groups.
The paper develops a new theory of double Johnson filtrations for mapping class groups.
Category theory enhances understanding of group-equivariant neural networks.
The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of quandles in relation to low dimensional cocycles are developed in parallel to gr…
Compute Bredon homology for a specific type of Artin groups.
The paper develops a theory of conformal density at infinity for groups with contracting elements.
Coarse geometry, and in particular coarse homotopy theory, has proven to be a powerful tool for approaching problems in geometric group theory and higher index theory. In this paper, we continue to develop theory in this area by proving a Coarse Lifting Lemma with respect to a certain class of bornologous surjective ma…
We compute the equivariant -homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological -theory of the reduced -algebra associated to the group, via the Baum-Connes conjecture. We show that, for any such reflection group…
Discrete Lagrange problems solved with Lie group constraints.
These are lectures on discrete groups of isometries of complex hyperbolic spaces, aimed to discuss interactions between the function theory on complex hyperbolic manifolds and the theory of discrete groups.
The paper extends knot theory to twisted virtual braids and links.
We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.
This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is …
This article will explore the K- and L-theory of group rings and their applications to algebra, geometry and topology. The Farrell-Jones Conjecture characterizes K- and L-theory groups. It has many implications, including the Borel and Novikov Conjectures for topological rigidity. Its current status, and many of its co…
Explores new perspectives in transverse index theory for Lie group actions.
We present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic Lie groups.
Survey on non-positively curved cube complexes and geometric group theory.