The Configuration Space of Regular Spherical Even Polygons

Abstract EN

Let a be a real number satisfying 0

We denote by Mna the configuration space of regular spherical n-gons with side lengths a.

In our previous paper, we determined χMna for odd n.

In this paper, we determine it for even n.

The main difference from our previous paper is given as follows.

When n is odd, we prove that Mna is obtained from Sn−3 by successive Morse surgeries.

On the other hand, when n is even, we show that Mna is obtained from Pn by successive Morse surgeries.

Here, Pn denotes the configuration space of equilateral n-gons in ℝ2, which has singular points when n is even.