Linear actions of $\mathbb{Z}/p\times\mathbb{Z}/p$ on $S^{2n-1}\times S^{2n-1}$

For an odd prime $p$ , we consider free actions of $(Z / p)^{2}$ on $S^{2 n - 1} \times S^{2 n - 1}$ given by linear actions of $(Z / p)^{2}$ on $R^{4 n}$ . 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.

Linear actions of $Z / p \times Z / p$ on $S^{2 n - 1} \times S^{2 n - 1}$

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Linear actions of $Z / p \times Z / p$ on $S^{2 n - 1} \times S^{2 n - 1}$

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Linear actions of Z/p×Z/pZ/p×Z/p on S2n−1×S2n−1S2n−1×S2n−1

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Linear actions of Z/p×Z/pZ/p×Z/p on S2n−1×S2n−1S2n−1×S2n−1

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Linear actions of $Z / p \times Z / p$ on $S^{2 n - 1} \times S^{2 n - 1}$

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AI智能校验

Linear actions of $Z / p \times Z / p$ on $S^{2 n - 1} \times S^{2 n - 1}$

讲解博客

AI智能校验