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Article overview
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Nonimmersions of RP^n implied by tmf, revisited | Donald M. Davis
; Mark Mahowald
; | Date: |
5 Apr 2007 | Subject: | Algebraic Topology (math.AT) | Abstract: | 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 imes
RP^infty) and tmf^*(CP^infty imes CP^infty) in positive dimensions. | Source: | arXiv, arxiv.0704.0798 | Services: | Forum | Review | PDF | Favorites |
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