The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the E-terms can be viewed as a type of local cohomology relative to a map or an object in the diagram.

We obtain generalizations of some results of Turaev from [Tur02]. Turaev’s results relate leading order terms of the Turaev torsion of closed, oriented, connected 3–manifolds to certain “determinants” derived from cohomology operations such as the alternate trilinear form on the first cohomology group given by cup product. These determinants unfortunately do not generalize directly to compact, ...

We define a relative version of tiling cohomology for the purpose of comparing the topology of tiling dynamical systems when one is a factor of the other. We illustrate this with examples, and outline a method for computing the cohomology of tiling spaces of finite type.

This paper uses a relative of BP -cohomology to prove a theorem in characteristic p algebra. Speci cally, we obtain some new necessary conditions for the existence of sums-of-squares formulas over elds of characteristic p > 2. These conditions were previously known in characteristic zero by results of Davis. Our proof uses a generalized etale cohomology theory called etale BP2.

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivari...

Let (M, g) be a complete, noncompact Riemannian manifold of finite volume. For w : M → (0,∞) a weighting function, the w weighted unreduced L2 cohomology is defined as the usual unreduced L2 cohomology except that dvol is replaced by the measure w dvol. This paper proves that in the case M = Γ\G/K is a locally symmetric space of nonpositive sectional curvature and arbitrary rank whereupon w(m) ...

Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations  from  the triangular Banach algebraof t...