K-theory and immersions of spatial polygon spaces

2019/01/13 by Davis, Donald M
#55N15 #55R80 #57R20 #57R42 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03983

Abstract

For ell a generic n-tuple of positive numbers, N(ell) denotes the space of isometry classes of oriented n-gons in R³ 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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