Topological representations of matroid maps

Matthew T. Stamps*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)265-287
Number of pages23
JournalJOURNAL OF ALGEBRAIC COMBINATORICS
Volume37
Issue number2
DOIs
Publication statusPublished - 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • Diagrams of spaces
  • Homotopy colimits
  • Matroids
  • Whitney numbers

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