On The Acyclic MacPhersonian

Abstract

In 2003 Daniel K. Biss published, in the Annals of Mathematics, what he thought was a solution of a long standing problem culminating a discovery by Gelfand and MacPherson. Six years later he was encouraged to publish an "erratum" of his prove, observed by Nikolai Mnev; up to now, the homotopy type of the MacPhersonian had remained a mistery... The aim of this lecture is to convince the attendee of the fact that, using a compleatly different aproach to those used before, we can prove that the acyclic MacPhersonian has the homotopy type of the affine Grassmannian.