Topological Methods in Nonlinear Analysis

Jiang-type theorems for coincidences of maps into homogeneous spaces

Daniel Vendrúscolo and Peter Wong

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Let $f,g\colon X\to G/K$ be maps from a closed connected orientable manifold $X$ to an orientable coset space $M=G/K$ where $G$ is a compact connected Lie group, $K$ a closed subgroup and $\dim X=\dim M$. In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\ne 0$ then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz, Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively. When $\dim X> \dim M$, we give conditions under which $N(f,g)=0$ implies $f$ and $g$ are deformable to be coincidence free.

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Topol. Methods Nonlinear Anal., Volume 31, Number 1 (2008), 151-160.

First available in Project Euclid: 13 May 2016

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Vendrúscolo, Daniel; Wong, Peter. Jiang-type theorems for coincidences of maps into homogeneous spaces. Topol. Methods Nonlinear Anal. 31 (2008), no. 1, 151--160.

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