Fusion systems and constructing free actions on products of spheres

Date
2012
Authors
Ünlü, Ö.
Yalçın, E.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Mathematische Zeitschrift
Print ISSN
0025-5874
Electronic ISSN
1432-1823
Publisher
Springer
Volume
270
Issue
3-4
Pages
939 - 959
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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Abstract

We show that every rank two p-group acts freely and smoothly on a product of two spheres. This follows from a more general construction: given a smooth action of a finite group G on a manifold M, we construct a smooth free action on M × S n1× ... × S nk when the set of isotropy subgroups of the G-action on M can be associated to a fusion system satisfying certain properties. Another consequence of this construction is that if G is an (almost) extra-special p-group of rank r, then it acts freely and smoothly on a product of r spheres. © 2011 Springer-Verlag.

Course
Other identifiers
Book Title
Keywords
Primary 57S25, Secondary 20D20
Citation
Published Version (Please cite this version)