Gr\"obner bases and some immersion theorems for Grassmann manifolds G_{3,n}

TL;DR

This paper computes a Gr"obner basis for the mod 2 cohomology of Grassmannian G_{3,n} and uses it with obstruction theory to derive new immersion theorems for these manifolds.

Contribution

It introduces a Gr"obner basis for the ideal in mod 2 cohomology of G_{3,n} and applies it to establish novel immersion results.

Findings

Derived a Gr"obner basis for the cohomology ideal

Established new immersion theorems for G_{3,n}

Connected algebraic computations with geometric immersion properties

Abstract

A Gr\"obner basis for the ideal determining mod 2 cohomology of Grassmannian G_{3,n} is obtained. This is used, along with the method of obstruction theory, to establish some new immersion results for these manifolds.