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Linear actions of \\( Z/p Z/p\\) on \\(S^2n-1 S^2n-1\\)
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Journal Article
Linear actions of \\( Z/p Z/p\\) on \\(S^2n-1 S^2n-1\\)
2024
Overview
For an odd prime \\(p\\), we consider free actions of \\(( Z_/p)^2\\) on \\(S^2n-1 S^2n-1\\) given by linear actions of \\(( Z_/p)^2\\) on \\( 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.
Publisher
Cambridge University Press
Subject
