Seminar

There are many examples of phenomena in chromatic homotopy theory that arise via inspiration from K-theory (i.e., height

1).  Good examples abound: the spectra eo_n generalizing ko, the redshift program, and so on.

In this talk, I'll present some new examples that are marginally geometric. Much of it will center on a cohomology theory which bears some formal resemblance to K-theory, but where the role of CP^\infty is played by K(Z, n+1).  For elements of this cohomology theory (analogues of virtual bundles), one can define K(n)-local Thom spectra and certain characteristic classes.  Some minor comments about the redshift program can also be made.

Mostly, I hope to formulate some coherent questions about both the geometric and homotopy-theoretic aspects of these constructions.