On properties of skew-framed immersions cobordism groups

TL;DR

This paper introduces a geometric approach to skew-framed manifolds to analyze stable homotopy groups and applies it to prove non-immersibility results for real projective spaces.

Contribution

It presents a new geometric technique for studying skew-framed manifolds and applies it to prove a classical non-immersibility theorem.

Findings

Developed a geometric method for skew-framed manifolds

Applied the method to prove non-immersibility of RP^10 in R^15

Provided insights into stable homotopy groups of Thom spaces

Abstract

In this paper, we introduce geometric technique of working with skew-framed manifolds. It allows us to study stable homotopy groups of some Thom spaces by geometric means. We schematically describe how our results (which are also of independent interest) can be applied to obtain a proof of the Baum-Browder theorem stating non-immersibility of $\RP^{10}$ to $\R^{15}$.