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
Laminations of a graph on a pair of pants
Ramassamy, Sanjay
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
UNDEFINED
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
2018-04-05
en