Some new nonimmersion results for real projective spaces

TL;DR

This paper employs tmf spectrum calculations to derive new nonimmersion results for real projective spaces, significantly expanding known results for large dimensions.

Contribution

It introduces novel tmf-cohomology computations leading to improved nonimmersion bounds for RP^n, covering many cases up to n as small as 113.

Findings

New nonimmersion results for RP^n for many n as small as 113

Expanded table of nonimmersion results for a range of n

New results cover 17% of n between 2^i and 2^i + 2^14 for i > 14

Abstract

We use the spectrum tmf to obtain new nonimmersion results for many real projective spaces RP^n for n as small as 113. The only new ingredient is some new calculations of tmf-cohomology groups. We present an expanded table of nonimmersion results. Our new theorem is new for 17% of the values of n between 2^i and 2^i + 2^14 for i > 14.