Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of are given, which are very similar to those of the relative Nielsen number N(f;X,A).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-1-5,
author = {Xuezhi Zhao},
title = {Minimal component numbers of fixed point sets},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {61-68},
zbl = {1052.55004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-1-5}
}
Xuezhi Zhao. Minimal component numbers of fixed point sets. Fundamenta Mathematicae, Tome 177 (2003) pp. 61-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-1-5/