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The homotopy type of the matroid Grassmannian

Author(s)
Biss, Daniel Kálmán, 1977-
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Michael J. Hopkins.
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M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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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).
 
Date issued
2002
URI
http://hdl.handle.net/1721.1/8400
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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