Mod 2 cohomology of combinatorial Grassmannians
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L. Anderson [1] ; J.F. Davis [2]
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[1] Binghamton University
Binghamton University
City of Binghamton, Estados Unidos
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[2] Indiana University, USA
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 8, Nº. 2, 2002, págs. 161-200
- Idioma: inglés
- DOI: 10.1007/s00029-002-8104-4
- Enlaces
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Resumen
Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.
