Lagrangian Matroids associated with Maps on Orientable Surfaces
Combinatorics
2007-05-23 v1
Abstract
The aim of the paper is to clarify the nature of combinatorial structures associated with maps on closed compact surfaces. We prove that maps give rise to Lagrangian matroids representable in a setting provided by cohomology of the surface with punctured points. Our proof is very elementary. We further observe that the greedy algorithm has a natural interpretation in this setting, as a `peeling' procedure which cuts the (connected) surface into a closed ring-shaped peel, and that this procedure is local.
Cite
@article{arxiv.math/0010236,
title = {Lagrangian Matroids associated with Maps on Orientable Surfaces},
author = {Richard F. Booth and Alexandre V. Borovik and Israel Gelfand},
journal= {arXiv preprint arXiv:math/0010236},
year = {2007}
}
Comments
12 pages. A rather more technical version of this paper, with the main proof reformulated in cohomological terms by David Stone, appeared as "Lagrangian Matroids and Cohomology" in Annals of Comb. 4 (2000), pp 171-182