Homotopy sphere representations for matroids

Details Homotopy sphere representations for matroids Homotopy sphere representations for matroids

2009-03-16

arxiv.org/abs/0903.2773v1

Mathematics

Combinatorics

Scientific paper

For any rank $r$ oriented matroid $M$, a construction is given of a "topological representation" of $M$ by an arrangement of homotopy spheres in a simplicial complex which is homotopy equivalent to $S^{r-1}$. The construction is completely explicit and depends only on a choice of maximal flag in $M$. If $M$ is orientable, then all Folkman-Lawrence representations of all orientations of $M$ embed in this representation in a homotopically nice way.

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