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Journal Articles Bulletin of the London Mathematical Society Year : 2020

Laminations of a graph on a pair of pants

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Abstract

A lamination of a graph embedded on a surface is a collection of pairwise 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 simplified variant 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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Dates and versions

ensl-01759975 , version 1 (05-04-2018)
ensl-01759975 , version 2 (25-06-2019)
ensl-01759975 , version 3 (27-10-2022)

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Sanjay Ramassamy. Laminations of a graph on a pair of pants. Bulletin of the London Mathematical Society, 2020, 52 (6), pp.1038-1052. ⟨10.1112/blms.12380⟩. ⟨ensl-01759975v3⟩
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