The homotopy type of the matroid Grassmannian
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50594992-MIT.pdf
Description
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2.46 MB
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f69bd182412686fc2ea0a71e94593040
Author(s)
Biss, Daniel Kálmán, 1977-
Advisor(s)
Michael J. Hopkins.
Date Issued
2002
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (p. 37-38).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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