Homology with models
Indecomposable racks of order .
Intersection Homology II.
Invariance proof of simplicial homology and cohomology groups without using subdivisions or axiomatic approach
Invariants in contact topology.
Inverse systems and pretopological spaces
Kazhdan-Lusztig Conjecture and Holonomic Systems.
Khovanov homology, its definitions and ramifications
Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these adaptations...
L1-cohomology of normal algebraic surfaces. I.
L2-Cohomologie des espaces stratifiés.
L2-cohomology and intersection homology of certain algebraic varieties with isolated singularities.
L²-homology and reciprocity for right-angled Coxeter groups
Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define -Betti numbers and an -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version of Poincaré...
Lefschetz fixed point theorem for intersection homology.
Linking pairings on singular spaces.
Localizing the Burnside Ring.
Non-standard analysis and homology
Normed combinatorial homology and noncommutative tori.
Note sur un résultat dans l'homologie sectionnelle
On a homology of algebras with unit
We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra with unit...
On fine shape theory II