Topological properties of matroids and related combinatorial structures

Goran Malic (University of Manchester)

Frank Adams 2,

Matroids are often introduced as combinatorial abstractions of linear (in)dependence in vector spaces. More formally, a matroid is a (finite and pure) abstract simplicial complex satisfying a certain exchange axiom. It is a geometrical object only formally; however by either introducing the concept of orientation, or by modifying slightly the exchange axiom, it becomes an interesting topological object. In this talk I shall give an overview of topological properties of oriented matroids, such as Mnev's Universality theorem and the Topological Representation Theorem of Folkman and Lawrence. I shall also discuss the so-called symplectic and Lagrangian matroids and their role in the stratification of various Grassmann varieties.
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