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Rank conditions for finite group actions on 4-manifolds

Part of: Topological manifolds

Published online by Cambridge University Press:  18 January 2021

Ian Hambleton  and
Semra Pamuk
Ian Hambleton*
Affiliation:
McMaster University, Hamilton, ON, Canada
Semra Pamuk
Affiliation:
Middle East Technical University, Ankara, Turkey e-mail: pasemra@metu.edu.tr
*
e-mail: hambleton@mcmaster.ca
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Abstract

Let M be a closed, connected, orientable topological $4$-manifold, and G be a finite group acting topologically and locally linearly on M. In this paper, we investigate the spectral sequence for the Borel cohomology $H^*_G(M)$ and establish new bounds on the rank of G for homologically trivial actions with discrete singular set.

Keywords

finite group actions4-manifoldsBorel spectral sequence

MSC classification

Primary: 57S17: Finite transformation groups
Secondary: 57S25: Groups acting on specific manifolds 57N65: Algebraic topology of manifolds

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 2 , April 2022 , pp. 550 - 572
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

This project was partially supported by NSERC Discovery Grant A4000. The first author wishes to thank the Max Planck Institut für Mathematik for its hospitality and support in November 2019. The second author was supported on sabbatical by METU and thanks McMaster University for its hospitality during the academic year 2018–19.

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