Gr\"obner bases for (all) Grassmann manifolds
Algebraic Topology
2013-05-20 v1 Commutative Algebra
Abstract
Grassmann manifolds are among the central objects in geometry and topology. The Borel picture of the mod 2 cohomology of is given as a polynomial algebra modulo a certain ideal . The purpose of this paper is to understand this cohomology via Gr\"obner bases. Reduced Gr\"obner bases for the ideals are determined. An application of these bases is given by proving an immersion theorem for Grassmann manifolds , which establishes new immersions for an infinite family of these manifolds.
Cite
@article{arxiv.1305.0420,
title = {Gr\"obner bases for (all) Grassmann manifolds},
author = {Zoran Z. Petrović and Branislav I. Prvulović and Marko Radovanović},
journal= {arXiv preprint arXiv:1305.0420},
year = {2013}
}