Related papers: Compactly supported cohomology of buildings

We propose to define the notion of abstract local cohomology functors. The derived functors of the ordinary local cohomology functor with support in the closed subset defined by an ideal and the generalized local cohomology functor…

We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.

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 cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…

We present sufficient conditions for topological stability of continuous functions $f:\mathbb{R}\to\mathbb{R}$ having finitely many local extrema with respect to averagings by discrete measures with finite supports.

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…

We show how the classical notions of cohomology with local coefficients, CW-complex, covering space, homeomorphism equivalence, simple homotopy equivalence, tubular neighbourhood, and spinning can be encoded on a computer and used to…

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact support, or as a subgroup of the homeomorphism group of its…

We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…

We compute the sheaf cohomology with constant $\mathbb{Z}_2$ coefficients of a concrete class of locally profinite sets of independent interest. We introduce $k$-sheer partitions to aid in constructions. It is also shown that questions of…

This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.

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

We construct a framework which gives intuitive representation of local cohomology groups. By defining the concrete mappings among them, we show their equivalence. As an application, we justify intuitive representation of Laplace…

We develop a method for subdividing polyhedral complexes in a way that restricts the possible recession cones and allows one to work with a fixed class of polyhedron. We use these results to construct locally finite completions of rational…

We develop a simple method of constructing topological spaces from countable posets with finite levels, one which applies to all second countable T_1 compacta. This results in a duality amenable to building such spaces from finite building…

Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…

In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic (J. Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups is…

Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…

The paper investigates two invariants for totally disconnected locally compact groups: the number of ends and the rational discrete cohomological dimension. For such a compactly generated group $G$ it is shown that its number of ends can be…

We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space $P(k\rho )$, of lines inside…