## Equivariant properties of symmetric products

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- by Stefan Schwede
- J. Amer. Math. Soc.
**30**(2017), 673-711 - DOI: https://doi.org/10.1090/jams/879
- Published electronically: February 24, 2017
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## Abstract:

The filtration of the infinite symmetric product of spheres by the number of factors provides a sequence of spectra between the sphere spectrum and the integral Eilenberg-Mac Lane spectrum. This filtration has received a lot of attention, and the subquotients are interesting stable homotopy types. While the symmetric product filtration has been a major focus of research since the 1980s, essentially nothing was known when one adds group actions into the picture. We investigate the equivariant stable homotopy types, for compact Lie groups, obtained from this filtration of infinite symmetric products of representation spheres. The situation differs from the non-equivariant case; for example, the subquotients of the filtration are no longer rationally trivial and on the zeroth equivariant homotopy groups an interesting filtration of the augmentation ideals of the Burnside rings arises. Our method is by global homotopy theory; i.e., we study the simultaneous behavior for all compact Lie groups at once.## References

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## Bibliographic Information

**Stefan Schwede**- Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
- MR Author ID: 623322
- Email: schwede@math.uni-bonn.de
- Received by editor(s): March 17, 2014
- Received by editor(s) in revised form: May 30, 2016
- Published electronically: February 24, 2017
- © Copyright 2017 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**30**(2017), 673-711 - MSC (2010): Primary 55P91
- DOI: https://doi.org/10.1090/jams/879
- MathSciNet review: 3630085