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Linear actions of $\mathbb {Z}/p\times \mathbb {Z}/p$
on $S^{2n-1}\times S^{2n-1}$![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240416053638415-0645:S0308210524000362:S0308210524000362_inline2.png)
Published online by Cambridge University Press: 16 April 2024
Abstract
For an odd prime $p$, we consider free actions of $(\mathbb {Z}_{/{p}})^2$
on $S^{2n-1}\times S^{2n-1}$
given by linear actions of $(\mathbb {Z}_{/{p}})^2$
on $\mathbb {R}^{4n}$
. Simple examples include a lens space cross a lens space, but $k$
-invariant calculations show that other quotients exist. Using the tools of Postnikov towers and surgery theory, the quotients are classified up to homotopy by the $k$
-invariants and up to homeomorphism by the Pontrjagin classes. We will present these results and demonstrate how to calculate the $k$
-invariants and the Pontrjagin classes from the rotation numbers.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
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