Relative stable (co)homology

Relative Compactness and Product Stable Quotient Maps

Relative Cohomology of Banach Algebras

Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...

Relative Hyperbolicity and Bounded Cohomology

Let Γ be a finitely generated group and Γ′ = {Γi | i ∈ I} be a family of its subgroups. We utilize the notion of tuple (Γ,Γ′, X,V ′) that makes the statements and arguments for the pair (Γ,Γ′) parallel to the non-relative case, and define the snake metric dς on the set of edges of a simplicial complex. The language of tuples and snake metrics seems to be convenient for dealing with relative hyp...

Relative cohomology of polynomial mappings

Let F be a polynomial mapping from C to C with n > q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F−1(∞) ”at infinity” and its cohomology. Let us fix a weighted homogeneous degree on C[x1, ..., xn] with strictly positive weights. The fibre at infinity is the zero set of the leading terms of the coordinate functions of F . We i...

Stable Operations in Generalized Cohomology