For a class H ε Hn+2(X; Z), we define twisted Morava K-theory K(n)*(X;H) at the prime 2, as well as an integral analogue. We explore properties of this twisted cohomology theory, studying a twisted Atiyah-Hirzebruch spectral sequence, a universal coefficient theorem (in the spirit of Khorami). We extend the construction to define twisted Morava E-theory, and provide applications to string theory and M-theory.
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© 2015 London Mathematical Society.