Problem of the Week
BUGCAT
Zassenhaus Conference
Hilton Memorial Lecture
BingAWM
Math Club
Matroid bundles are combinatorial objects which mimic real vector bundles. Gelfand and MacPherson used oriented matroids in bundle theory to get a combinatorial formula for the rational Pontryagin classes. MacPherson abstracted this into a bundle theory called ``matroid bundles.
In the first talk I will show how to construct a map from the set of isomorphism classes of rank-k vector bundles over a regular cell complex B to the set of isomorphism classes of rank-k matroid bundles over B.
In the second talk I will discuss the Spherical Quasifibration Theorem, which associates a spherical quasifibration to a matroid bundle, and the Comparison Theorem, which shows that the composition of these two associations is the forgetful map given by deleting the zero section.
I will also give some important consequences of these results in characteristic classes.
These talks are based on the paper of L. Anderson and J. Davis, ``Mod 2 cohomology of Combinatorial Grassmannians
, Selecta Mathematica, New Series, 8 (2002).