The homotopy type of the matroid Grassmannian
Author(s)Biss, Daniel Kálmán, 1977-
Massachusetts Institute of Technology. Dept. of Mathematics.
Michael J. Hopkins.
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In this thesis, I establish a homotopy equivalence between the matroid Grassmannian [parallel] MacP(k, n) [parallel] and the real Grassmannian G(k, n) of k-planes in [Real set]n. This is accomplished by finding a Schubert stratification of the former space and analyzing its relationship to the ordinary Schubert cell decomposition of the Grassmannian. Since the classifying spaces for rank k matroid bundles and rank k vector bundles are, respectively, obtained by taking colimits of the above spaces as n grows, this result provides a natural equivalence between the functors of matroid bundles and vector bundles. This, in turn, has implications for the interplay between combinatorics and topology, particularly concerning the Gelfand-MacPherson combinatorial formula for rational Pontrjagin classes.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.Includes bibliographical references (p. 37-38).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology