Deformations of bordered Riemann surfaces and associahedral polytopes

Details Deformations of bordered Riemann surfaces and associahedral polytopes Deformations of bordered Riemann surfaces and associahedral polytopes

2010-02-08

arxiv.org/abs/1002.1676v1

Notices of the AMS 58 (2011) 530-541

Mathematics

Algebraic Geometry

25 pages, 31 figures

Scientific paper

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. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structures are related to generalizations of associahedra and multiplihedra.

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