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Tuesday, September 22, 2015

**Abstract:** Complex cobordism and its relatives, the Johnson-Wilson theories, E(n), carry an action of C_2 by complex conjugation. Taking fixed points of the latter yields Real Johnson-Wilson theories, ER(n). These can be seen as generalizations of real K-theory and are similarly amenable to computations. We will outline their properties, describe a generalization of the \eta-fibration, and discuss recent computations of the ER(n)-cohomology of some well-known spaces, including CP^\infty.