Twisted Morava K-theory and connective covers of Lie groups

Understand

Twisted Morava K-theory, along with computational techniques, including a universal coefficient theorem and an Atiyah-Hirzebruch spectral sequence, was introduced by Craig Westerland and the first author.

• We employ these techniques to compute twisted Morava K-theory of all connective covers of the stable orthogonal group and stable unitary group, and their classifying spaces, as well as spheres and Eilenberg-MacLane spaces.
• This extends to the twisted case some of the results of Ravenel and Wilson and of Kitchloo, Laures, and Wilson for Morava K-theory.
• This also generalizes to all chromatic levels computations by Khorami (and in part those of Douglas) at chromatic level one, i.e.