Signatures of singular branched covers.
Classical knot and link concordance.
A TQFT for Wormhole cobordisms over the field of rational functions
We consider a cobordism category whose morphisms are punctured connected sums of ’s (wormhole spaces) with embedded admissibly colored banded trivalent graphs. We define a TQFT on this cobordism category over the field of rational functions in an indeterminant A. For r large, we recover, by specializing A to a primitive 4rth root of unity, the Witten-Reshetikhin-Turaev TQFT restricted to links in wormhole spaces. Thus, for r large, the rth Witten-Reshetikhin-Turaev invariant of a link in some wormhole...
On the Slice Genus of Knots.
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.
Integral lattices in TQFT
On the slice genus of links.
The Homflypt skein module of a connected sum of 3-manifolds.
3-manifold invariants and periodicity of homology spheres.
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