Degree of $T$-equivariant maps in $\mathbb R^n$
Volume 77 / 2007
Banach Center Publications 77 (2007), 147-159
MSC: 47H11.
DOI: 10.4064/bc77-0-11
Abstract
A special case of $G$-equivariant degree is defined, where $G=\mathbb Z_2$, and the action is determined by an involution $T:\mathbb R^p\oplus\mathbb R^q\to\mathbb R^p\oplus\mathbb R^q$ given by $T(u,v)=(u,-v)$. The presented construction is self-contained. It is also shown that two $T$-equivariant gradient maps $f,g:(\mathbb R^n,S^{n-1})\to(\mathbb R^n,\mathbb R^n\setminus\{0\})$ are $T$-homotopic iff they are gradient $T$-homotopic. This is an equivariant generalization of the result due to Parusi/nski.
