A Relation Between Existence of Real Symmetric Nonsingular Bilinear Maps and the Antisymmetric Index of Projective Spaces

TL;DR

This paper presents a new proof connecting the existence of real symmetric nonsingular bilinear maps with the antisymmetric index of projective spaces, utilizing integral cohomology and group actions.

Contribution

It offers a novel proof of an embedding theorem for real projective spaces based on cohomological and group action techniques.

Findings

New proof of an embedding theorem for real projective spaces

Establishes a link between bilinear maps and antisymmetric indices

Utilizes integral cohomology and group actions in the proof

Abstract

We obtain a new proof, using integral cohomology and group actions, of an old embedding theorem for real projective spaces.