The gap-labelling group, which provides the set of possible values of the integrated density of states on gaps in the spectrum of a Hamiltonian describing particles in a tiling, is frequently related to the cohomology of the tiling. We present explicit results for the cohomology of many well-known tilings obtained from the cut and projection method with codimension 2, including the (generalized...

Let ( X , J ) be an almost complex manifold with a (smooth) involution σ : → such that Fix ≠ ∅ . Assume is conjugation, i.e., the differential of anti-commutes The space P m = S × / ∼ where v x − was referred to as generalized Dold manifold. above definition admits obvious generalization much wider class spaces are arbitrary topological spaces. resulting will called space. When and CW complexes...

let $s$ be an inverse semigroup and let $e$ be its subsemigroup of idempotents. in this paper we define the $n$-th module cohomology group of banach algebras and show that the first module cohomology group $hh^1_{ell^1(e)}(ell^1(s),ell^1(s)^{(n)})$ is zero, for every odd $ninmathbb{n}$. next, for a clifford semigroup $s$ we show that $hh^2_{ell^1(e)}(ell^1(s),ell^1(s)^{(n)})$ is a banach space,...

It has been shown recently that the geometry of D-branes in general topologically twisted (2, 2) sigma-models can be described in the language of generalized complex structures. On general grounds such D-branes (called generalized complex (GC) branes) must form a category. We compute the BRST cohomology of open strings with both ends on the same GC brane. In mathematical terms, we determine spa...

We explain how the approach of André and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.

We construct a ring structure on complex cobordism tensored with Q, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-dimensional topological field theory taking values in a category of spectra.

Unitary representations of the fundamental group of a Kähl-er manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to poly-stable Higgs bundles. In this paper we find the objects corresponding to affine representations: the linear part gives a Higgs bundle and the translation part corresponds to an element of a generalized...

This paper is devoted to the horizontal (“characteristic”) cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov C-spectral sequence and Krasilshchik’s C-cohomology are obtained. As an application of general theory, the examples of an evolution equation and a p-form gaug...