Twisted Morava K-theory and E-theory
arXiv:1109.3867 · doi:10.1112/jtopol/jtv020
Abstract
For an integral cohomology class H of degree n+2 on a space X, 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, study a twisted Atiyah-Hirzebruch spectral sequence, and give 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.
30 pages. Updated: Results for Morava E-theory have been corrected to only apply to deformations of the "standard" Morava K-theory. Additionally, they have been extended to work at all primes. Typos have been fixed and minor changes in terminology made. The paper has been accepted for publication by the Journal of Topology
References in corpus (10)
- Twisted differential String and Fivebrane structures
- Units of ring spectra and Thom spectra
- Commutativity conditions for truncated Brown-Peterson spectra of height 2
- Twisted K-theory, old and new
- Twisted topological structures related to M-branes
- A Higher Twist in String Theory
- A universal coefficient theorem for twisted K-theory
- The Morava E-theory of Eilenberg-Mac Lane spaces
- Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory
- K-theory of the moduli of bundles over a Riemann surface and deformations of the Verlinde algebra
Cited by in corpus (11)
- Ramond-Ramond fields and twisted differential K-theory
- Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
- Quantization via Linear homotopy types
- Spectral sequences in smooth generalized cohomology
- M-Theory with Framed Corners and Tertiary Index Invariants
- Bordism for the 2-group symmetries of the heterotic and CHL strings
- Twisted iterated algebraic K-theory and topological T-duality for sphere bundles
- Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
- Twisted smooth Deligne cohomology
- Twisted Morava K-theory and connective covers of Lie groups
- The Smith Fiber Sequence and Invertible Field Theories