Intersection Numbers of Polygon Spaces

Details Intersection Numbers of Polygon Spaces Intersection Numbers of Polygon Spaces

2007-09-13

arxiv.org/abs/0709.2097v2

Mathematics

Symplectic Geometry

31 pages, 1 figure. Revision: added a new section relating our results to other formulas

Scientific paper

We study the intersection ring of the space $\M(\alpha_1,...,\alpha_m)$ of polygons in $\R^3$. We find homology cycles dual to generators of this ring and prove a recursion relation in $m$ (the number of steps) for their intersection numbers. This result is analog of the recursion relation appearing in the work of Witten and Kontsevich on moduli spaces of punctured curves and on the work of Weitsman on moduli spaces of flat connections on two-manifolds of genus $g$ with $m$ marked points. Based on this recursion formula we obtain an explicit expression for the computation of the intersection numbers of polygon spaces and use it in several examples. Among others, we study the special case of equilateral polygon spaces (where all the $\alpha_i$ are the same) and compare our results with the expressions for these particular spaces that have been determined by Kamiyama and Tezuka. Finally, we relate our explicit formula for the intersection numbers with the generating function for intersection pairings of the moduli space of flat connections of Yoshida, as well as with equivalent expressions for polygon spaces obtained by Takakura and Konno through different techniques.

Affiliated with

Also associated with

No associations

Rating

Intersection Numbers of Polygon Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intersection Numbers of Polygon Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intersection Numbers of Polygon Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215176