Nonimmersions of RP^n implied by tmf, revisited

dc.creatorDavis, Donald M.
dc.creatorMahowald, Mark
dc.date2007-04-05
dc.date.accessioned2026-07-07T07:55:31Z
dc.date.available2026-07-07T07:55:31Z
dc.descriptionIn 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.description35 pages; author produced PDF available at http://www.lehigh.edu/~dmd1/overlook4.pdf
dc.identifierhttps://arxiv.org/abs/0704.0798
dc.identifierhttp://arxiv.org/abs/0704.0798
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126997
dc.subjectAlgebraic Topology
dc.subject57R42; 55N20
dc.titleNonimmersions of RP^n implied by tmf, revisited
dc.typetext

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