Nonimmersions of RP^n implied by tmf, revisited
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
In a 2002 paper, the authors and Bruner used the new spectrum tmf to obtain some new nonimmersions of real projective spaces. In this note, we complete/correct two oversights in that paper.
The first is to note that in that paper a general nonimmersion result was stated which yielded new nonimmersions for RP^n with n as small as 48, and yet it was stated there that the first new result occurred when n=1536. Here we give a simple proof of those overlooked results.
Secondly, we fill in a gap in the proof of the 2002 paper. There it was claimed that an axial map f must satisfy f^*(X)=X_1+X_2. We realized recently that this is not clear. However, here we show that it is true up multiplication by a unit in the appropriate ring, and so we retrieve all the nonimmersion results claimed in the original paper.
Finally, we present a complete determination of tmf^{8*}(RP^\infty\times RP^\infty) and tmf^*(CP^\infty\times CP^\infty) in positive dimensions.
35 pages; author produced PDF available at http://www.lehigh.edu/~dmd1/overlook4.pdf
35 pages; author produced PDF available at http://www.lehigh.edu/~dmd1/overlook4.pdf