Finite symmetries of S4
-
Weimin Chen
,
Sławomir Kwasik
Abstract
This paper discusses topological and locally linear actions of finite groups on S4. Local linearity of the orientation preserving actions on S4 forces the group to be a subgroup of SO(5). On the other hand, orientation reversing topological actions of “exotic” groups G (i.e., G ¬⊂ O(5)) on S4 are constructed, and local linearity and stable smoothability of the actions are studied.
Funding source: NSF
Award Identifier / Grant number: DMS-1065784
Funding source: Simons Foundation
Award Identifier / Grant number: 281810
Funding source: NSF FRG
Award Identifier / Grant number: DMS-1065905
Part of this work was initiated when the first and the second named authors attended the FRG workshop “The Topology and Invariants of Smooth 4-Manifolds” in Miami, March 12–16, 2012. We thank the organizer Nikolai Saveliev for his hospitality and are grateful for the financial support through the NSF FRG grant DMS-1065905 and the University of Miami. All authors would like to thank Rafal Komendarczyk for the helping hand with the typesetting. Finally, the authors would like to thank the referee for the many suggestions which have improved considerably the exposition of the paper. In particular, we would like to thank the referee for directing our attention to Problem 2.
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
Artikel in diesem Heft
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
