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arXiv · 1901.03983

K-theory and immersions of spatial polygon spaces

Donald M Davis
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Abstract

For ell a generic n-tuple of positive numbers, N(ell) denotes the space of isometry classes of oriented n-gons in R^3 with side lengths specified by ell. We determine the algebra K(N(ell)) and use this to obtain nonimmersions of the 2(n-3)-manifold N(ell) in Euclidean space for several families of ell. We also use obstruction theory to tell exactly when N(ell) immerses in R^{4n-14} for two families of ell.

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Donald M Davis. 2019-01-13. K-theory and immersions of spatial polygon spaces. https://arxiv.org/abs/1901.03983

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