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 RPn 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)=X1+X2. 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 2002 paper. Finally, we completely determine tmf8*(RP∞×RP∞) and tmf*(CP∞×CP∞) in positive dimensions.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 3, pp.151-179.
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