相关论文: Quotient Cohomology for Tiling Spaces

We compute the cohomology with trivial coefficients of two graded infinite-dimensional Lie algebras of maximal class, give explicit formulas for their representative cocycles. Also we discuss the relations with combinatorics and…

We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…

This is a short survey of Riemannian geometric applications of Lp-cohomology of thick spaces, p not equal to 2.

This article is part introduction and part survey to the mathematical area centered around local cohomology.

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…

As a generalization of our previous paper [GK], we formulate a residue formula and some simple behaviors of equivariant quantum cohomology applying to compute the quantum cohomology of partial flag manifolds $F_{k_1,\cdots , k_l} $with a…

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…

Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the integral cohomology of the locally symmetric space Gamma\D. The…

The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are…

We describe a general setting for the definition of semi-infinite cohomology of finite dimensional algebras, and provide its categorical interpretation. We apply this interpretation to compute semi-infinite cohomology of some modules over…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).

In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational…

To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on…

Complexity one spaces are an important class of examples in symplectic geometry. Karshon and Tolman classify them in terms of combinatorial and topological data. In this paper, we compute the equivariant cohomology for any complexity one…

We compute the $p$-adic \'etale and the pro-\'etale cohomologies of the Drinfeld half-space of any dimension. The main input is a new comparison theorem for the $p$-adic pro-\'etale cohomology of $p$-adic Stein spaces.

In this paper, we attempt to determine the quantum cohomology of projective bundles over the projective space P^n. In contrast to the previous examples, the relevant moduli spaces in our case frequently do not have expected dimensions. It…

As a part of our program for Geometric Arithmetic, we develop an arithmetic cohomology theory for number fields using theory of locally compact groups.

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…