MIT Topology Seminar: Computational Methods for Higher Real K-Theory with Applications to tmf (Mike Hill)

MIT Topology Seminar

Monday, May 1, 2006
Room 26-210, 3:15pm

Mike Hill will speak on:

Computational Methods for Higher Real K-Theory with Applications to tmf

Abstract: Long ago, Mahowald computed the ko homology of the classifying space of the group \Sigma_2. This computation has has a number of interesting and important ramifications, as it has been used in such varied contexts as demonstrating the survival of an infinite family of elements in the stable stem readily expressible in the Adams spectral sequence. In this talk, we will generalize this result to all primes, indicating how the compute the eo_{p-1} homology of B\Sigma_p at the prime p. We will show that such groups are computable using an Adams spectral sequence which naturally generalizes that for ko homology, and we will prove that the Hopf algebras involved are of the form conjectured by the author and Andre Henriques.