Geodesic
Topological representations of matroid maps
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 2, pp. 265-287.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid arises from the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we use a construction of Engström to show that structure-preserving maps between matroids induce topological mappings between their representations; a result previously known only in the oriented case. Specifically, we show that weak maps induce continuous maps and that this process is a functor from the category of matroids with weak maps to the homotopy category of topological spaces. We also give a new and conceptual proof of a result regarding the Whitney numbers of the first kind of a matroid.
Keywords: matroids, diagrams of spaces, homotopy colimits, Whitney numbers 
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Stamps, Matthew T. Topological representations of matroid maps. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 2, pp. 265-287. http://geodesic.mathdoc.fr/item/JAC_2013__37_2_a5/