Spherical 2-categories and 4-manifold Invariants

m at h . Q A ] 2 5 O ct 1 99 8 Spherical 2 - categories and 4 - manifold invariants

m at h . Q A ] 2 3 M ay 1 99 8 Spherical 2 - categories and 4 - manifold invariants

Finite groups, spherical 2-categories, and 4-manifold invariants

In this paper we define a class of state-sum invariants of compact closed oriented piece-wise linear 4-manifolds using finite groups. The definition of these state-sums follows from the general abstract construction of 4-manifold invariants using spherical 2-categories, as we defined in [32], although it requires a slight generalization of that construction. We show that the state-sum invariant...

An introduction to the Seiberg-Witten equations on symplectic manifolds∗

The Seiberg-Witten equations are defined on any smooth 4-manifold. By appropriately counting the solutions to the equations, one obtains smooth 4-manifold invariants. On a symplectic 4-manifold, these invariants have a symplectic interpretation, as a count of pseudoholomorphic curves. This allows us to transfer information between the smooth and symplectic categories in four dimensions. In the ...

Invariants of Piecewise - Linear 3 - Manifolds

The purpose of this paper is to present an algebraic framework for constructing invariants of closed oriented 3-manifolds. The construction is in the spirit of topological field theory and the invariant is calculated from a triangulation of the 3-manifold. The data for the construction of the invariant is a tensor category with a condition on the duals, which we have called a spherical category...