Stiefel-Whitney classes and immersions of orientable and Spin manifolds

Donald M. Davis; W. Stephen Wilson

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arXiv · 2011.00974

Stiefel-Whitney classes and immersions of orientable and Spin manifolds

Donald M. Davis·W. Stephen Wilson

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Abstract

We determine a nice simple formula for the largest Euclidean space for which there is an orientable n-manifold with a nonimmersion detected by Stiefel-Whitney classes. For Spin manifolds, we prove the analogue of the upper bound and establish the complete answer for n<24 and n=33,34. Results similar to many of these were obtained some 50 years ago, but in a much less tractable form. The sharp results for Spin manifolds require detailed calculations of ko-homology groups of mod-2 Eilenberg-MacLane spaces.

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Donald M. Davis, W. Stephen Wilson. 2020-11-02. Stiefel-Whitney classes and immersions of orientable and Spin manifolds. https://arxiv.org/abs/2011.00974

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