×

zbMATH — the first resource for mathematics

The Lefschetz number of self-maps of Lie groups. (English) Zbl 0689.55005
Summary: In this note we present a simple approach to the Lefschetz number for the self-maps of Lie groups. As an application it is proved that for any map f: \(G\to G\) of a compact connected Lie group G, there is a solution to \((f(x))^ k=x\) for some \(k\leq \lambda +1\), where \(\lambda\) is the rank of the group G.

MSC:
55M20 Fixed points and coincidences in algebraic topology
PDF BibTeX XML Cite
Full Text: DOI