The Hochschild and (cotriple) cyclic homologies of crossed modules of (notnecessarily-unital) associative algebras are investigated. Wodzicki’s excision theorem is extended for inclusion crossed modules in the category of crossed modules of algebras. The cyclic and cotriple cyclic homologies of crossed modules are compared in terms of long exact homology sequence, generalising the relative cycl...

We obtain the equivariant K-homology of the classifying space EW for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of EW in terms of Coxeter cells. Our calculations amount to the K-theory of the reduced C∗-algebra of W , via the Baum-Connes assembly map.

We prove that for certain classes of graded algebras (Koszul, local, cellular), infinite global dimension implies that Hochschild homology does not vanish in high degrees, provided the characteristic of the ground field is zero. Our proof uses Igusa’s formula relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant.

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...

This paper generalizes the Max-Flow Min-Cut (MFMC) theorem from the setting of numerical capacities to cellular sheaves of semimodules on directed graphs. Motivating examples of semimodules include probability distributions, multicommodity capacity constraints, and logical propositions. Directed algebraic topology provides the tools necessary for capturing the salient information in such a gene...

We report experiments designed to test homology dependence for gene conversion between duplicated chromosomal sequences in cultured mammalian cells. The experimental system is such that gene conversion events not associated with reciprocal exchange are recoverable. For this study four plasmids were constructed. Each contains a different duplication of the herpes simplex virus thymidine kinase (...

Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten-Floer homology to obtain an invariant of homology 3-spheres which lives in the S 1-equivariant graded suspension category. We also define a relative invariant of four-manifolds with boundary and use it to give new proofs to some results of Frøyshov from [Fr].

background: no data is available on morphology and genetic characteristics of echinococcus granulosus derived from donkeys of iran, despite of its existence in donkeys.in the present study morphometric variations of the rostellar hooks of protoscoleces and genotype characteristics of hydatid cyst of donkey from iran were determined. methods: protoscoleces prepared from hydatid cyst of donkey of...