Laminations of a graph on a pair of pants - ENS de Lyon - École normale supérieure de Lyon Access content directly
Preprints, Working Papers, ... Year : 2018

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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Dates and versions

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

Identifiers

  • HAL Id : ensl-01759975 , version 1

Cite

Sanjay Ramassamy. Laminations of a graph on a pair of pants. 2018. ⟨ensl-01759975v1⟩
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