Defects, super-Poincaré line bundle and fermionic T-duality

On Fermionic T-duality of Sigma modes on AdS backgrounds

We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma models on AdS backgrounds. We show that the sigma model on AdS5 × S1 background is self-dual under fermionic T-duality. We also construct new integrable sigma models on AdS2 ×CPn. These backgrounds could be realized as supercosets of SU supergroups for arbitrary n, but could also be realized as supercosets of OSp superg...

Poincaré Duality Algebras Mod Two

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...

Poincaré Duality and Commutative Differential Graded Algebras

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré du-ality in the same dimension. This has application in particular to the study of CDGA models of configuration spaces on a closed manifold.

Twisted K-theory and Poincaré duality

Using methods of KK-theory, we generalize Poincaré K-duality to the framework of twisted K-theory.