Homology cobordism group of homology 3-spheres.
Homology Comodules.
Homology Equivalences and a Technique of Ganea.
Homology exponents for -spaces.
Homology fibrations and “group-completion” revisited.
Homology Fibrations and the "Group-Completion" Theorem.
Homology functors on shape categories
Homology groups and eight-term exact sequences
Homology groups of semicubical sets.
Homology of braid groups and their generalizations
In the paper we give a survey of (co)homologies of braid groups and groups connected with them. Among these groups are pure braid groups and generalized braid groups. We present explicit formulations of some theorems of V. I. Arnold, E. Brieskorn, D. B. Fuks, F. Cohen, V. V. Goryunov and others. The ideas of some proofs are outlined. As an application of (co)homologies of braid groups we study the Thom spectra of these groups.
Homology of Deleted Product Spaces.
Homology of Function Spaces.
Homology of -fold groupoids.
Homology of representable sets
We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.
Homology of the double and triple loop space of SO (n).
Homology Operations in the Eilenberg-Moore Spectral Sequence.
Homology theory for real analytic and semianalytic sets
Homology theory for the set-theoretic Yang-Baxter equation and knot invariants from generalizations of quandles
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
Homology theory in the alternative set theory I. Algebraic preliminaries
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative -group), is introduced. Commutative -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...
Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms
Homology functor in the spirit of the AST is defined, its basic properties are studied. Eilenberg-Steenrod axioms for this functor are formulated and established.