Twisted smooth Deligne cohomology
arXiv:1706.02742 · doi:10.1007/s10455-017-9583-z
Abstract
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has not been done to Deligne cohomology, although existence is known at a general abstract level. We work out what it means to twist Deligne cohomology, by taking degree one twists of both integral cohomology and de Rham cohomology. We present the main properties of the new theory and illustrate its use with examples and applications. Given how versatile Deligne cohomology has proven to be, we believe that this explicit and utilizable treatment of its twisted version will be useful.
21 pages, title modified to include smooth, references added, minor corrections and additions, published version
References in corpus (1)
Cited by in corpus (4)
- The character map in (twisted differential) non-abelian cohomology
- Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
- Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
- Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence