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Laminations of a graph on a pair of pants

Abstract : A lamination of a graph embedded on a surface is a collection of pair-wise disjoint non-contractible simple closed curves drawn on the graph. In the case when the surface is a sphere with three punctures (a.k.a. a pair of pants), we first identify the lamination space of a graph embedded on that surface as a lattice polytope, then we characterize the polytopes that arise as the lamination space of some graph on a pair of pants. This characterizes the image of a purely topological version of the spectral map for the vector bundle Laplacian for a flat connection on a pair of pants. The proof uses a graph exploration technique akin to the peeling of planar maps.
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Contributor : Sanjay Ramassamy Connect in order to contact the contributor
Submitted on : Tuesday, June 25, 2019 - 5:46:38 PM
Last modification on : Thursday, March 17, 2022 - 10:08:19 AM

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Sanjay Ramassamy. Laminations of a graph on a pair of pants. Bulletin of the London Mathematical Society, London Mathematical Society, 2020, 52 (6), pp.1038-1052. ⟨10.1112/blms.12380⟩. ⟨ensl-01759975v2⟩

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