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.
Quantum cohomology connects quantum physics with classical math.
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been expl…
We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show th…
We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent useful tools in studying non Kähler geometry. We give an overview on the comparis…
The paper computes KV cochain differentials and their geometric implications.
Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.
Standard cohomology of Courant algebroids identified via minimal models.
Study cohomology jump loci in 3-manifolds, focusing on Alexander polynomial.
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provi…
We study quasi-isometry invariants of Gromov hyperbolic spaces, focussing on the l_p-cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous l_p-cohomology, thereby obtaining information about the l…
Kotschick and Morita recently discovered factorisations of characteristic classes of transversally symplectic foliations that yield new characteristic classes in foliated cohomology. We describe an alternative construction of such factorisations and construct examples of topologically trivial foliated vector bundles fo…
Defines new gradings on Khovanov homology for surface embeddings.
We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural connection between 2-dimensional field theories and elliptic cohomology originally due…
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which accommodates the KdV equation and other well known integrable systems. In the case of qua…
We show that a flat principal bundle with compact connected structure group and its adjoint bundles of Lie groups have the same cohomology as the trivial bundle, which is done by proving they satisfy the condition for the Leray-Hirsch theorem. This information has been used to construct a cohomology class of the adjoin…
New method uses cohomology to quantify molecular similarity.
We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.
The paper explores higher fixed point theorems for foliations with applications to rigidity and integrality.
Paper extends Poisson-Lichnerowicz cohomology to scalar difference Hamiltonian operators.
Aim of this note is to extract cohomological information about the manifold from the topology of the target manifold N. For special conditions, a monomorphism is constructed.
Every rack provides a set-theoretic solution of the Yang-Baxter equation. This article examines the deformation theory of within the space of Yang-Baxter operators over a ring $\A$, a problem initiated by Freyd and Yetter in 1989. As our main result we classify deformations in the modular case, which ha…
The technique of generating families produces obstructions to the existence of embedded Lagrangian cobordisms between Legendrian submanifolds in the symplectizations of 1-jet bundles. In fact, generating families may be used to construct a TQFT-like theory that, in addition to giving the aforementioned obstructions, yi…
Aim of this note is to gain cohomological information about the infinite-dimensional manifold of asymptotically fixed embeddings of M into N from the topology of the target manifold N. This paper has been withdrawn by the author due a conceptual mistake.
Nontrivial Massey products found on compact Kähler manifolds.
Paper constructs fold maps with useful singular value sets.
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…
The paper solves a general case of the cohomological relative index problem for foliations.
In this paper we suggest a new general formalism for studying the invariants of polyhedra and manifolds comming from the theory of von Neumann algebras. First, we examine generality in which one may apply the construction of the extended abelian category, which was suggested in the previous publications of the author, …
Study of fold maps and Reeb spaces via surgery operations.
Survey on finite group actions on manifolds.
We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action θof the maximal torus T ^{k} on G/H. We obtain explicit formula for the cobordism class of such manifold through the weights of the action θat the identity fixed poin…
We extend the Yang-Baxter cocycle invariants for virtual knots by augmenting Yang-Baxter 2-cocycles with cocycles from a cohomology theory associated to a virtual biquandle structure. These invariants coincide with the classical Yang-Baxter cocycle invariants for classical knots but provide extra information about virt…
Extends cohomology theory for infinite volume transformation groups.
New cohomology theory for Lie 2-algebras extends classical theory.
In this work we deal with left invariant complex and symplectic structures on simply connected four dimensional solvable real Lie groups. We search the general form of such structures, when they exist and we make use of this information to determine all left invariant Kaehler structures. Finally, as an appendix we comp…
Generics extended to new cohomologies.
The paper studies cohomology of complex manifolds using Morse-Novikov and Dolbeault-Morse-Novikov theories.
Classifies states of four rebits using group theory.
In this short note we define a new cohomology for a Lie algebroid , that we call the \emph{twisted cohomology} of by an odd cocycle in the Lie algebroid cohomology of . We proof that this cohomology only depends on the Lie algebroid cohomology class of the odd cocycle $…
The article examines twisted cohomologies on algebraic and analytic varieties.
New homology theories for orbifolds and weighted polyhedra.
Study cohomology of hemistrict Lie 2-algebras, proving isomorphic results.
New cohomology theories for heaps and ternary operations linked to group cohomology.
Study characterizes cohomology of Vaisman manifolds, linking Bott-Chern and Dolbeault numbers.
Proves a vanishing property for symplectic manifold cohomology.
In this paper we define a new cohomology of a smooth manifold called Lichnerowicz type cohomology attached to a function. Firstly, we study some basic properties of this cohomology as: a de Rham type isomorphism, dependence on the function, singular forms, relative cohomology, Mayer-Vietoris sequence, homotopy invarian…
De Rham theorem extended to Orlicz cohomology.
New proof of blow-up formula for Morse-Novikov cohomology.