3/1/2012

Nitu Kitchloo
Johns Hopkins University

Stable and unstable properties of real Johnson-Wilson spectra

I will try to describe the properties of certain spectra known as real Johnson-Wilson spectra, which are obtained as fixed points of involutions on the usual Johnson Wilson spectra. These spectra, that go by the symbol ER(n), have several intriguing properties. For example, they are periodic and they support a self map whose cofiber is the Johnson Wilson spectrum E(n). This makes them computationally amenable. I'll describe how one can use ER(2) to prove some non-immersion results for real projective spaces. Unstably, the spaces in the omega spectra for ER(n) admit product splittings that behave in interesting ways under periodicity. If time permits, I'll go into some interesting questions including the question on ER(n) orientation of bundles. This is ongoing joint work with Steve Wilson.