HAL CCSD
Laminations of a graph on a pair of pants
Ramassamy, Sanjay
Unité de Mathématiques Pures et Appliquées (UMPA-ENSL) ; École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
ensl-01759975
https://ens-lyon.hal.science/ensl-01759975
https://ens-lyon.hal.science/ensl-01759975v1/document
https://ens-lyon.hal.science/ensl-01759975v1/file/PantsLaminations.pdf
https://ens-lyon.hal.science/ensl-01759975
2018
en
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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.
2018-04-05
info:eu-repo/semantics/OpenAccess