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