## Any finite group acts freely and homologically trivially on a product of spheres

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- by James F. Davis PDF
- Proc. Amer. Math. Soc.
**144**(2016), 379-386 Request permission

## Abstract:

The main theorem states that if $K$ is a finite CW-complex with finite fundamental group $G$ and universal cover homotopy equivalent to a product of spheres $X$, then $G$ acts smoothly and freely on $X \times S^n$ for any $n$ greater than or equal to the dimension of $X$. If the $G$-action on the universal cover of $K$ is homologically trivial, then so is the action on $X \times S^n$. Ünlü and Yalçın recently showed that any finite group acts freely, cellularly, and homologicially trivially on a finite CW-complex which has the homotopy type of a product of spheres. Thus every finite group acts smoothly, freely, and homologically trivially on a product of spheres.## References

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## Additional Information

**James F. Davis**- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 194576
- Email: jfdavis@indiana.edu
- Received by editor(s): September 21, 2012
- Received by editor(s) in revised form: December 28, 2013
- Published electronically: September 11, 2015
- Additional Notes: This research was supported by the National Science Foundation grant DMS-1210991. The research was inspired by a visit to Boğaziçi University, where the visit was supported by the Boğaziçi University Foundation.
- Communicated by: Daniel Ruberman
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**144**(2016), 379-386 - MSC (2010): Primary 57S25; Secondary 57Q40, 57R80
- DOI: https://doi.org/10.1090/proc/12435
- MathSciNet review: 3415604