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A classification of cohomology transfers for ramified covering maps

Marcelo A. Aguilar, Carlos Prieto (2006)

Fundamenta Mathematicae

We construct a cohomology transfer for n-fold ramified covering maps. Then we define a very general concept of transfer for ramified covering maps and prove a classification theorem for such transfers. This generalizes Roush's classification of transfers for n-fold ordinary covering maps. We characterize those representable cofunctors which admit a family of transfers for ramified covering maps that have two naturality properties, as well as normalization and stability. This is analogous to Roush's...

Homotopy orbits of free loop spaces

Marcel Bökstedt, Iver Ottosen (1999)

Fundamenta Mathematicae

Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors Ω λ ( R ) and ℓ(R) together with algebra homomorphisms e : Ω λ ( R ) H * ( Λ X ) and ψ : ( R ) H * ( E S 1 × S 1 Λ X ) . When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.

On symplectic cobordism of real projective plane.

Malkhaz Bakuradze (2000)

Publicacions Matemàtiques

This note answers a question of V. V. Vershinin concerning the properties of Buchstaber's elements Θ2i+1(2) in the symplectic cobordism ring of the real projective plane. It is motivated by Roush's famous result that the restriction of these elements to the projective line is trivial, and by the relationship with obstructions to multiplication in symplectic cobordism with singularities.

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