Deformations of bordered Riemann surfaces and associahedral polytopes

Understand

We consider the moduli space of bordered Riemann surfaces with boundary and marked points.

• Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds.
• We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling.
• Our main result classifies all such spaces that can be realized as convex polytopes.