The Bruhat decomposition of real Grassmann manifolds

Date: Mar 2017

Abstract: We study the Grassmann manifold Gk of all k-dimensional subspaces of Rn. The Cartan embedding Gk⊂O(n) realizes Gk as a subspace of Sln(R) and we study the decomposition inherited from the classical Bruhat decomposition. We prove that this defines a CW structure and determine the incidence numbers between cells.

This paper is not quite finished - I'm currently still looking for a more elegant description of the incidence numbers before submitting it.

Documentation of the minimal resolution

Date: Sep 2001

Abstract:Extract of the minimal resolution up to dimension 210

Computing May resolutions

File(s): maydes.dvi
Date: Jun 1996

Abstract:Attempt to compute the May spectral sequences of sub Hopf algebras of the Steenrod algebra.

Minimal May resolutions for the mod 2 homology algebras of E6, E7 and E8

File(s): maye8.dvi
Date: Aug 1997

Abstract: We use the May resolution approach to describe a resolution of the homology algebras of the title.

Computing cohomology groups from May resolutions

File(s): e8comp.dvi
Date: Sep 1998

Abstract:A note that simplifies the description of the May resolution of the H*(Ej).