Lagrangian Matroids associated with Maps on Orientable Surfaces

Details Lagrangian Matroids associated with Maps on Orientable Surfaces Lagrangian Matroids associated with Maps on Orientable Surfaces

2000-10-25

arxiv.org/abs/math/0010236v1

Mathematics

Combinatorics

12 pages. A rather more technical version of this paper, with the main proof reformulated in cohomological terms by David Ston

Scientific paper

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.

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