Chern numbers of the moduli space of spatial polygons

Abstract

Let \mathscr{M}_n (n≥3) be the moduli space of spatial polygons with n edges. We consider the case of odd n. First we establish a procedure to determine the Chern numbers of \mathscr{M}_n. Next we follow the procedure and get a description of \mathscr{M}_n (n≤9) in the complex cobordism group Ω_2n−6^U. Finally we determine some characteristic numbers of \mathscr{M}_n. In particular, we calculate the Todd genus of \mathscr{M}_n by showing that \mathscr{M}_n is birationally equivalent to CPⁿ⁻³.