𝐾-theory and immersions of spatial polygon spaces

Abstract

AbstractFor {\ell} a generic n-tuple of positive numbers, {N(\ell)} denotes the space of isometry classes of oriented n-gons in {\mathbb{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 {\mathbb{R}^{4n-14}} for two families of {\ell}’s.