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.
Develops deformation theory for mapping spaces related to Morse theory and Bott-Thom isomorphism.
Isomorphic cosymplectomorphism groups imply diffeomorphic manifolds.
New knot quandles distinguish ribbon knots with isomorphic groups.
Geometric duality connects graph isomorphism and knot equivalence.
In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a ch…
The paper explores isomorphisms on isoparametric hypersurfaces in spheres, leading to new geometric structures.
We construct examples of knots that have isomorphic nth-order Alexander modules, but non-isomorphic nth-order linking forms, showing that the linking forms provide more information than the modules alone. This generalizes work of Trotter, who found examples of knots that have isomorphic classical Alexander modules, but…
Proves regularity of isomorphisms between hyperbolic 3-manifolds.
We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group , there is a one-to-one correspondence between the set of isomorphism classes of connected Lie groups which are locally isomorphic to and a union of certain quotients of noncom…
Non-isomorphic groups with similar profinite completions found.
The paper studies the cut locus of submanifolds in Riemannian manifolds, providing geometric and topological insights.
Paper solves isomorphism problem for specific Baumslag-Solitar groups.
We consider the notion of stable isomorphism of bundle gerbes. It has the consequence that the stable isomorphism classes of bundle gerbes over a manifold M are in bijective correspondence with H^3(M, Z). Stable isomorphism sheds light on the local theory of bundle gerbes and enables us to develop a classifying theory …
New benchmarks improve model performance by accounting for isomorphism classes in multi-relational datasets.
This is the fourth of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an an a…
Undecidability proved for DG algebras problems.
A subgroup of a Kac-Moody group is called bounded if it is contained in the intersection of two finite type parabolic subgroups of opposite signs. In this paper, we study the isomorphisms between Kac-Moody groups over arbitrary fields of cardinality at least 4, which preserve the set of bounded subgroups. We show that …
The paper disproves a conjecture about isomorphic subgroups in finite groups.
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension …
Unique vertical isomorphisms between Fedosov dg manifolds are proven for Lie pairs.
If M is a riemannian manifold, then the inclusion of the complex of coclosed harmonic forms into the de Rham complex induces a linear isomorphism in cohomology. If M has at most countably many connected components, this linear isomorphism is a Frechet isomorphism.
Proves regularity of isomorphisms between hyperbolic 3-manifolds.
Projective manifolds with specific bundles are isomorphic to simpler spaces.
The paper characterizes generalized Alexander quandles and counts them up to 127.
Survey on proof of homology isomorphism between two complex theories.
Homologies of Jones and partition algebras match cyclic and symmetric groups.
We give the classification of solvable and splitting Lie triple system and it turn that, up to isomorphism there exist 7 non isomorphic canonical Lie triple systems and 6 non isomorphic splitting canonical Lie triple systems and find the solvable Lie algebras associated.
In this project we further investigate the idea of reducing the dimensionality of datasets using a Borel isomorphism with the purpose of subsequently applying supervised learning algorithms, as originally suggested by my supervisor V. Pestov (in 2011 Dagstuhl preprint). Any consistent learning algorithm, for example kN…
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it …
The isomorphism problem for [free abelian]-by-free groups is unsolvable.
Formality of Dolbeault DGAs on complex nilmanifolds restricted to tori.
We find a new algebra isomorphic to Khovanov's arc algebra in characteristic 2.
In this paper we construct arbitrarily large families of smooth projective varieties and closed Riemannian manifolds that share many algebraic and analytic invariants. For instance, every non-arithmetic, closed hyperbolic --manifold admits arbitrarily large collections of non-isometric finite covers which are strong…
Paper shows 3D hyperbolic manifolds are uniquely identified by their finite groups.
We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups…
The paper establishes isomorphisms and constructs colored versions of Lawrence representations.
Penrose transform tells us that there is an isomorphism of the kernel of an invariant differential operator studied in the paper [TS] and sheaf cohomology of some vector bundle on twistor space. The point of this paper is to write down this isomorphism explicitly. Explicit form of the isomorphism will be crucial for fu…
The aim of this paper is to relate Thurston's metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will give a new formula for Thurston's asymmetric metric for surfaces with punctures. We also update some results of Sorvali on boundary isomorp…
The study generalizes Blaschke curvature for higher-dimensional webs and identifies infinite classes of isomorphism.
We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for certain amalgamations of free groups: the direct limits of two such diagrams are iso…
The study enumerates virtual quandles up to isomorphism.
We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of …
We show that two Alexander biquandles M and M' are isomorphic iff there is an isomorphism of Z[s,1/s,t,1/t]-modules h:(1-st)M --> (1-st)M' and a bijection g:O_s(A) --> O_s(A') between the s-orbits of sets of coset representatives of M/(1-st)M and M'/(1-st)M' respectively satisfying certain compatibility conditions.
We solve the isomorphism problem for the whole class of Lins-Mandel gems (graphs encoded manifolds). We also present certain homeomorphisms of branched cyclic coverings of two-bridge hyperbolic links. As a consequence, we prove that, in in a wide subset of interesting cases, the isomorphism conditions for Lins-Mandel g…
We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of Lie algebraic approach to space. First we show that if the Lie algebras of smooth sections of two Atiyah algebroids are isomorphic, then the corresponding base manifolds are necessarily diffeomorphic. Further, w…
We prove that if a normal subgroup of the extended mapping class group of a closed surface has an element of sufficiently small support then its automorphism group and abstract commensurator group are both isomorphic to the extended mapping class group. The proof relies on another theorem we prove, which states that ma…
Two markets should be considered isomorphic if they are financially indistinguishable. We define a notion of isomorphism for financial markets in both discrete and continuous time. We then seek to identify the distinct isomorphism classes, that is to classify markets. We classify complete one-period markets. We define …
Classifies genus-1 holomorphic Lefschetz pencils up to smooth isomorphism.