Coincidences for maps of spaces with finite group actions

Let G be a finite group acting freely in a Hausdorff, paracompact, connected and locally pathwise connected topological space X such that H i ( X, Z)=0 for 0< i< m and H m+1 ( G, Z)≠0. Let f :X→Y be a map of X to a finite k-dimensional CW-complex Y. We show that if m⩾| G| k, then f has a ( H,...

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Bibliographic Details
Published in:Topology and its applications 2004-11, Vol.145 (1), p.61-68
Main Authors: Gonçalves, Daciberg L., Jaworowski, Jan, Pergher, Pedro L.Q., Volovikov, A.Yu
Format: Article
Language:English
Subjects:
( H, G)-coincidence point
Classifying space
G-action
Join space
Spectral sequence
Transfer
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Summary:Let G be a finite group acting freely in a Hausdorff, paracompact, connected and locally pathwise connected topological space X such that H i ( X, Z)=0 for 0< i< m and H m+1 ( G, Z)≠0. Let f :X→Y be a map of X to a finite k-dimensional CW-complex Y. We show that if m⩾| G| k, then f has a ( H, G)-coincidence point for some nontrivial subgroup H of G.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2004.05.010