Related papers: Co-Euler structures on bordisms

We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of…

Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under…

We obtain a class of locally symetric Kaehler Einstein structures on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained class of Kaehler Einstein structures depends on one essential…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

This is a survey paper of author's results on cobordism groups and semigroups of fold maps and simple fold maps. The results include: establishing a relation between fold maps and immersions through geometrical invariants of cobordism…

Covariant Hom-bimodules are introduced and the structure theory of them in the Hom-setting is studied in a detailed way. The category of bicovariant Hom-bimodules is proved to be a (pre)braided monoidal category and its structure theory is…

Recently, some concepts such as Hom-algebras, Hom-Lie algebras, Hom-Lie admissible algebras, Hom-coalgebras are studied and some of classical properties of algebras and some geometric objects are extended on them. In this paper by recall…

The subject for investigation in this note is concerned with holomorphic Poisson structures on nilmanifolds with abelian complex structures. As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

We provide a framework for the study of structured manifolds with singularities and their locally determined invariants. This generalizes factorization homology, or topological chiral homology, to the setting of singular manifolds equipped…

An alternative proof of bornological Verdier duality for complex manifolds, as proven initially by Prosmans & Schneiders is given, using Schneider's theory of quasi-abelian homological algebra, and the theory of residues and duality.

We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of isomorphism between holomorphic Poisson manifolds, which is…

We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces

We prove the equivariant holomorphic Morse inequalities for a holomorphic torus action on a holomorphic vector bundle over a compact Kahler manifold when the fixed-point set is not necessarily discrete. Such inequalities bound the twisted…

In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…

We define the notion of mirror of a Calabi-Yau manifold with a stable bundle in the context of type II strings in terms of supersymmetric cycles on the mirror. This allows us to relate the variation of Hodge structure for cohomologies…

In this paper we continue the investigation of Loday's Leibniz cohomology as a new invariant for differentiable manifolds. In particular the Leibniz coboundary of a k-tensor (in the sense of differential geometry) is computed in a local…

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…

We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott-Chern cohomology in terms of Betti…

We introduce the notion of Rota-Baxter coalgebra which can be viewed as the dual notion of Rota-Baxter algebra. We provide some concrete examples and establish various properties of this new object. We also consider comodules over…