English

Gr\"obner bases for (all) Grassmann manifolds

Algebraic Topology 2013-05-20 v1 Commutative Algebra

Abstract

Grassmann manifolds Gk,nG_{k,n} are among the central objects in geometry and topology. The Borel picture of the mod 2 cohomology of Gk,nG_{k,n} is given as a polynomial algebra modulo a certain ideal Ik,nI_{k,n}. The purpose of this paper is to understand this cohomology via Gr\"obner bases. Reduced Gr\"obner bases for the ideals Ik,nI_{k,n} are determined. An application of these bases is given by proving an immersion theorem for Grassmann manifolds G5,nG_{5,n}, which establishes new immersions for an infinite family of these manifolds.

Keywords

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}
}
R2 v1 2026-06-22T00:10:09.370Z