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Group actions on spheres with rank one isotropy


Authors: Ian Hambleton and Ergün Yalçın
Journal: Trans. Amer. Math. Soc. 368 (2016), 5951-5977
MSC (2010): Primary 20J05, 55U15, 57S17, 18Gxx
DOI: https://doi.org/10.1090/tran/6567
Published electronically: October 20, 2015
MathSciNet review: 3458403
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Abstract: Let $ G$ be a rank two finite group, and let $ \mathcal {H}$ denote the family of all rank one $ p$-subgroups of $ G$ for which $ \operatorname {rank}_p(G)=2$. We show that a rank two finite group $ G$ which satisfies certain explicit group-theoretic conditions admits a finite $ G$-CW-complex $ X\simeq S^n$ with isotropy in $ \mathcal {H}$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear $ G$-CW-complex examples.


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Additional Information

Ian Hambleton
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Email: hambleton@mcmaster.ca

Ergün Yalçın
Affiliation: Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
Email: yalcine@fen.bilkent.edu.tr

DOI: https://doi.org/10.1090/tran/6567
Received by editor(s): April 9, 2014
Received by editor(s) in revised form: September 17, 2014, and December 14, 2014
Published electronically: October 20, 2015
Additional Notes: This research was partially supported by NSERC Discovery Grant A4000. The second author was partially supported by TÜBİTAK-TBAG/110T712.
Article copyright: © Copyright 2015 American Mathematical Society