On the Connectivity of Cobordisms and Half-Projective TQFT's

Details On the Connectivity of Cobordisms and Half-Projective TQFT's On the Connectivity of Cobordisms and Half-Projective TQFT's

1996-03-22

arxiv.org/abs/q-alg/9603017v1

Commun.Math.Phys. 198 (1998) 535-590

Physics

High Energy Physics

High Energy Physics - Theory

55 pages, Latex

Scientific paper

10.1007/s002200050487

We consider a generalization of the axioms of a TQFT, so called half-projective TQFT's, with an anomaly, $x^{\mu}$, in the composition law. $\mu$ is a coboundary on the cobordism categories with non-negative, integer values. The element $x$ of the ring over which the TQFT is defined does not have to be invertible. In particular, it may be 0. This modification makes it possible to extend quantum-invariants, which vanish on $S^1\times S^2$, to non-trivial TQFT's. (A TQFT in the sense of Atiyah with this property has to be trivial all together). Under a few natural assumptions the notion of a half-projective TQFT is shown to be the only possible generalization. Based on separate work with Lyubashenko on connected TQFT's, we construct a large class of half-projective TQFT's with $x=0$. Their invariants vanish on $S^1\times S^2$, and they coincide with the Hennings invariant for non-semisimple Hopf algebras. Several toplogical tools that are relevant for vanishing properties of such TQFT's are developed. They are concerned with connectivity properties of cobordisms, as for example maximal non-separating surfaces. We introduce in particular the notions of ``interior'' homotopy and homology groups, and of coordinate graphs, which are functions on cobordisms with values in the morphisms of a graph category. For applications we will prove that half-projective TQFT's with $x=0$ vanish on cobordisms with infinite interior homology, and we argue that the order of divergence of the TQFT on a cobordism in the ``classical limit'' can be estimated by the rank of its maximal free interior group.

Affiliated with

Also associated with

No associations

Rating

On the Connectivity of Cobordisms and Half-Projective TQFT's does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Connectivity of Cobordisms and Half-Projective TQFT's, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Connectivity of Cobordisms and Half-Projective TQFT's will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-421356