𝐾-theory and immersions of spatial polygon spaces

Abstract

For ℓ an n-tuple of positive numbers, N pℓq denotes the space of isometry classes of oriented n-gons in R 3 with side lengths specified by ℓ. If ℓ is generic, N pℓq is a 2pn´3q-manifold. We determine the algebra KpN pℓqq and use this to obtain nonimmersions of N pℓq in Euclidean space for several families of ℓ. We also use obstruction theory to tell exactly when N pℓq immerses in R 4n´14 for two families of ℓ's.