Nonimmersions of real projective spaces implied by tmf

This paper, coauthored with Robert Bruner and Mark Mahowald, appeared in the Proceedings of the JAMI Conference held at Johns Hopkins University in March, 2000. These proceedings were published in American Math Society Contemporary Mathematics. 293 (2002) 45-68. See the dvi file or ps file.

Abstract: Recently Hopkins and Mahowald constructed a new 2-primary ring spectrum tmf, satisfying H^*(tmf) = A//A2. We use tmf to obtain new results regarding nonimmersions of real projective spaces in Euclidean space. The method is to say enough about the tmf-cohomology of a product of real projective spaces to obtain nonexistence of certain axial maps.