Homology, Homotopy and Applications

Volume 10 (2008)

Number 3

Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson

The second real Johnson-Wilson theory and nonimmersions of $RP^n$, Part II

Pages: 269 – 290

DOI: https://dx.doi.org/10.4310/HHA.2008.v10.n3.a12


Nitu Kitchloo (Department of Mathematics, University of California at San Diego)

W. Stephen Wilson (Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A.)


This paper is a continuation of the study begun in the previous paper with the same title. We analyze $ER(2)^{16*+\,8}(RP^{2n})$ and compute $ER(2)^*(RP^{16K+1})$, and use these to prove more nonimmersion theorems for $RP^n$, including many in fairly low dimensions. In particular, we get 12 new nonimmersion results for $RP^n$ where $n < 192$, the range included in the tables Don Davis keeps. These complement the 10 already found in the first paper.


Real projective space, nonimmersions, Johnson-Wilson theories

2010 Mathematics Subject Classification

55N20, 55N91, 55T25, 57R42

Published 1 January 2008