Nonimmersions of RP^n implied by tmf, revisited
| dc.creator | Davis, Donald M. | |
| dc.creator | Mahowald, Mark | |
| dc.date | 2007-04-05 | |
| dc.date.accessioned | 2026-07-07T07:55:31Z | |
| dc.date.available | 2026-07-07T07:55:31Z | |
| dc.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. | |
| dc.description | 35 pages; author produced PDF available at http://www.lehigh.edu/~dmd1/overlook4.pdf | |
| dc.identifier | https://arxiv.org/abs/0704.0798 | |
| dc.identifier | http://arxiv.org/abs/0704.0798 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126997 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R42; 55N20 | |
| dc.title | Nonimmersions of RP^n implied by tmf, revisited | |
| dc.type | text |