3-dimensional defect TQFTs and their tricategories

Two Dimensional Tqfts

Three-dimensional 2-framed TQFTS and surgery

The notion of 2-framed three-manifolds is defined. The category of 2-framed cobordisms is described, and used to define a 2-framed three-dimensional TQFT. Using skeletonization and special features of this category, a small set of data and relations is given that suffice to construct a 2-framed three-dimensional TQFT. These data and relations are expressed in the language of surgery.

Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras

We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs). These are defined on open-closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that have a particular global structure in order to model the smooth topology of open and closed string worldsheets. We show that the category of open-closed TQFTs is equivalent to the category...

Links, Quantum Groups and Tqfts

X iv :q -a lg /9 50 60 02 v2 3 1 Ju l 1 99 5 Abstract. The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given. The quantum group Uq(sl2), which gives rise to the Jones polynomial, is constructed explicitly. The 3-m...

Integrality for Tqfts

We discuss two ways that the ring of coeffients for a TQFT can be reduced if one may restrict somewhat the allowed cobordisms. When we apply both methods to a TQFT associated to SO(3) and an odd prime p, we obtain a functor from a somewhat restricted cobordism category to the category of free finitely generated modules over a ring of cyclotomic integers : Z[ζp], if p ≡ −1 (mod 4), and Z[ζ4p], i...