Mod 2 cohomology of combinatorial Grassmannians |
| |
Authors: | L Anderson JF Davis |
| |
Institution: | Department of Mathematics, Binghamton University, P.O. Box 6000, Binghamton, NY 13902-6000, USA, e-mail: laura@math.binghamton.edu, US Department of Mathematics, Indiana University, Bloomington, IN 47405, USA,? e-mail: jfdavis@indiana.edu, US
|
| |
Abstract: | 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. |
| |
Keywords: | , Oriented matroid, MacPhersonian, vector bundle, matroid bundle, |
本文献已被 SpringerLink 等数据库收录! |
|