Topological representations of matroids
Combinatorics
2007-05-23 v2 Commutative Algebra
Geometric Topology
Abstract
There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky's enumeration of the cells of the arrangement still holds. An application of the theory shows that all minimal cellular resolutions of matroid Steiner ideals are bounded subcomplexes of homotopy sphere arrangements of the given matroid. As a result the Betti numbers of the ideal are computed and seen to be equivalent to Stanley's formula in the special case of face ideals of independence complexes of matroids.
Cite
@article{arxiv.math/0208157,
title = {Topological representations of matroids},
author = {Edward Swartz},
journal= {arXiv preprint arXiv:math/0208157},
year = {2007}
}
Comments
21 pages, 4 figures Numerous typographical and notational errors corrected. Theorem 7.2 and the following discussion corrected