Volume 13, issue 5 (2013)

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Borsuk–Ulam theorems and their parametrized versions for spaces of type $(a,b)$

Denise de Mattos, Pedro Luiz Q Pergher and Edivaldo L dos Santos

Algebraic & Geometric Topology 13 (2013) 2827–2843
Abstract

Let $X$ be a space of type $\left(a,b\right)$ equipped with a free $G$–action, with $G={ℤ}_{2}$ or ${S}^{1}$. In this paper, we prove some theorems of Borsuk–Ulam-type and the corresponding parametrized versions for such $G$–spaces.

Keywords
Space of type $(a, b)$, parametrized Borsuk–Ulam theorem, Leray–Serre spectral sequence, Borel construction, characteristic polynomial, free action, equivariant map
Mathematical Subject Classification 2010
Primary: 55M20
Secondary: 55R91, 55R25