Bulletin of the Belgian Mathematical Society - Simon Stevin

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

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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 $f:X\rightarrow M$ be a continuous map where $M$ is a connected $m$-manifold (orientable if $p>2$) and $f^* (V_k) = 0$, for $k\geq 1$, where $V_k$ are the $Wu$ classes of $M$. Suppose that $\ind X\geq n> (|G|-r)m$, where $r=\frac{|G|}{p}$. In this work, we estimate the cohomological dimension of the set $A(f,H,G)$ 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 $r$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 4 (2017), 567-579.

Dates
First available in Project Euclid: 4 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1515035007

Mathematical Reviews number (MathSciNet)
MR3743262

Zentralblatt MATH identifier
06848701

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25] 52A35: Helly-type theorems and geometric transversal theory
Secondary: 55M35: Finite groups of transformations (including Smith theory) [See also 57S17] 55S35: Obstruction theory

Keywords
$(H,G)$-coincidence $G$-action topological Tverberg theorem

Citation

de Mattos, Denise; dos Santos, Edivaldo L.; Souza, Taciana O. $(H,G)$-coincidence theorems for manifolds and a topological Tverberg type theorem for any natural number $r$. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 567--579. https://projecteuclid.org/euclid.bbms/1515035007


Export citation