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.
Researchers use Gysin sequence to show sl(N) homology of T(2,m) is cohomology of SU(N) representations.
Part 2 discusses compatibility between analytic and topological Gysin maps.
Generalizes double transgression formulas on complex manifolds.
We use the theory of pseudo-holomorphic quilts to establish a counterpart, in symplectic Floer homology, to the Gysin sequence for the homology of a sphere-bundle. In a motivating class of examples, this "symplectic Gysin sequence" is precisely analogous to an exact sequence describing the behaviour of Seiberg-Witten m…
New Smith-Gysin sequence for non-semi-free actions without semi-free condition.
In this paper we construct Cech cohomology groups that form a Gysin-type long exact sequence for principal torus bundles. This sequence is modeled on a de Rham cohomology sequence published in earlier work by Bouwknegt, Hannabuss and Mathai, which was developed to compute the global properties of T-duality in the prese…
New method defines Gysin maps for stratified spaces, preserving signatures.
We give two generalizations of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calcula…
The paper proves a pointwise Gysin formula for vector bundles and applies it to show positivity of polynomials.
Study spherical T-duality and Massey products in iterated sphere bundles.
We develop a new approach to the pulling back fixed point theorem of W. Browder and use it in order to prove various generalizations of this result.
In this paper we use tools from differential topology to give a geometric description of cohomology for Hilbert manifolds. Our model is Quillen's geometric description of cobordism groups for finite dimensional smooth manifolds \cite{Q}. Quillen stresses the fact that this construction allows the definition of Gysin ma…
The blow-down map is studied in Lie algebroid cohomology.
This paper introduces persistent equivariant cohomology and applies it to circle actions.
In this paper we study the topological T-dual of spaces with a non-free circle action mainly using the stack theory method of Bunke and co-workers \cite{Bunke1}. We first compare three formalisms for obtaining the Topological T-dual of a semi-free -space in a simple example. Then, we calculate the T-dual of genera…
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
Reciprocity laws for line bundles on circle fibrations over complex manifolds.
Spherical T-duality for iterated sphere bundles
Study normal bundle and deformation to get new pushforward maps.
In this paper, we investigate the behaviour of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specificially with the Chas-Sullivan product and the corresponding coproduct and module structures. We prove compatibility for two kinds of fibre bundl…
Develops a new theory of localization in algebraic geometry.
Paper develops equivariant basic cohomology for Lie groupoids.
Isomorphic cosymplectomorphism groups imply diffeomorphic manifolds.
Proves a Thom isomorphism for foliated differential forms.
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.
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.