# Stable and Unstable Properties of Real Johnson-Wilson Spectra

# 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.