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Fixed-point sets of smooth actions on spheres

Published online by Cambridge University Press:  30 November 2007

Masaharu Morimoto
Masaharu Morimoto
Affiliation:
morimoto@ems.okayama-u.ac.jpDepartment of Environmental and Mathematical Sciences, Faculty of Environmental Science and Technology, Okayama University, Tsushimanaka 3-1-1, Okayama, 700-8530Japan
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Abstract

Given a group, it is a basic problem to determine which manifolds can occur as a fixed-point set of a smooth action of this group on a sphere. The current article answers this problem for a family of finite groups including perfect groups and nilpotent Oliver groups. We obtain the answer as an application of a new deleting and inserting theorem which is formulated to delete (or insert) fixed-point sets from (or to) disks with smooth actions of finite groups. One of the keys to the proof is an equivariant interpretation of the surgery theory of S. E. Cappell and J. L. Shaneson, for obtaining homology equivalences.

Keywords

Equivariant surgerysurgery obstructionstrong gap conditionfixed pointsphere

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Type
Research Article
Information
Journal of K-Theory , Volume 1 , Issue 1 , February 2008 , pp. 95 - 128
Copyright
Copyright © ISOPP 2008

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