Lifting Arc Diagrams Under Branched Covers: An Inverse Problem and its Solution
Combinatorics
2020-09-15 v1 Geometric Topology
Abstract
A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably solve the membership problem of the set of weighted arc diagrams on a given surface which can be obtained by lifting a weighted arc diagram on a bigon. We provide a brute force solution in the general case, and an efficient solution when the input arc diagram is a triangulation.
Keywords
Cite
@article{arxiv.2009.05608,
title = {Lifting Arc Diagrams Under Branched Covers: An Inverse Problem and its Solution},
author = {Cyrus Peterpaul},
journal= {arXiv preprint arXiv:2009.05608},
year = {2020}
}