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Linear actions of $\mathbb {Z}/p\times \mathbb {Z}/p$
on $S^{2n-1}\times S^{2n-1}$
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 16 April 2024, pp. 1-14
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- Article
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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.
