TFT Construction of RCFT correlators. V: Proof of modular invariance and factorisation.
The parity of the Maslov index and the even cobordism category
We give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over ℝ. We define an index two subcategory (the even subcategory) of a 3-dimensional cobordism category. The objects of the category are surfaces equipped with Lagrangian subspaces of their real first homology. This generalizes a result of the first author where surfaces are equipped with Lagrangian subspaces of their rational first homology.
The reduction of quantum invariants of 4-thickenings
We study the sensibility of an invariant of 2-dimensional CW complexes in the case when it comes as a reduction (through a change of ring) of a modular invariant of 4-dimensional thickenings of such complexes: it is shown that if the Euler characteristic of the 2-complex is greater than or equal to 1, its invariant depends only on homology. To see what is happening when the Euler characteristic is smaller than 1, we use ideas of Kerler and construct, from any tortile category, an invariant of 4-thickenings...
The superpolynomial for knot homologies.
Torsion, TQFT, and Seiberg-Witten invariants of 3-manifolds.
TQFT's and gerbes.
Universal manifold pairings and positivity.