(H, G)-coincidence theorems for manifolds and a topological Tverberg type theorem for any natural number r

Author(s)

de Mattos, Denise ; dos Santos, Edivaldo L. ; Souza, Taciana O.

• Document type: Journal article
• Source: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN; v. 24, n. 4, p. 13-pg., 2017-01-01.

Abstract

Let X be a paracompact space, let G be a finite group acting freely on X and let H a cyclic subgroup of G of prime order p. Let f : X -> M be a continuous map where M is a connected m-manifold (orientable if p > 2) and f* (V-k) = 0, for k >= 1, where V-k are the Wu classes of M. Suppose that ind X >= n > (vertical bar G vertical bar - r)m, where r = vertical bar G vertical bar/p. In this work, we estimate the cohomological dimension of the set Ay, H, G) of (H, G)-coincidence points of f. Also, we estimate the index of a (H, G) -coincidence set in the case that H is a p-torus subgroup of a particular group G and as application we prove a topological Tverberg type theorem for any natural number r. Such result is a weak version of the famous topological Tverberg conjecture, which was proved recently fail for all r that are not prime powers. Moreover, we obtain a generalized Van Kampen-Flores type theorem for any integer r. (AU)

• FAPESP's process: 12/24454-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/24845-0 - On Lusternik-Schnirelmann category, ideal-value genus and global classification of isolated singularities
• Grantee: Denise de Mattos
• Support Opportunities: Regular Research Grants