Periodic twisted cohomology and T-duality

Details Periodic twisted cohomology and T-duality Periodic twisted cohomology and T-duality

2008-05-10

arxiv.org/abs/0805.1459v2

Asterisque 337 (2011)

Mathematics

Algebraic Topology

128 pages; v2: small corrections (e.g. of typos), version to appear in Asterisque

Scientific paper

The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topological stacks with emphasis on the construction of the sheaf theory operations in unbounded derived categories, elements of Verdier duality and integration. The main result is the construction of a functorial periodization functor associated to a U(1)-gerbe. As applications we verify the $T$-duality isomorphism in periodic twisted cohomology and in periodic twisted orbispace cohomology.

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