1,601 research outputs found
Deformations of bordered Riemann surfaces and associahedral polytopes
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.Comment: 25 pages, 31 figure
Cubic complexes and finite type invariants
Cubic complexes appear in the theory of finite type invariants so often that
one can ascribe them to basic notions of the theory. In this paper we begin the
exposition of finite type invariants from the `cubic' point of view. Finite
type invariants of knots and homology 3-spheres fit perfectly into this
conception. In particular, we get a natural explanation why they behave like
polynomials.Comment: Published by Geometry and Topology Monographs at
http://www.maths.warwick.ac.uk/gt/GTMon4/paper14.abs.htm
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