Recurrence relations and asymptotics\\ for four-manifold invariants

Recurrence Relations and Asymptotics for Four - Manifold

The polynomial invariants qd for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the polynomials. As an application, one can read off a lower bound for the genera of embedded surfaces from the asymptotics of qd for large d. The relations are proved u...

Asymptotics of Orthogonal Polynomials via Recurrence Relations

Asymptotics of a Slow Manifold

Approximately invariant elliptic slow manifolds are constructed for the Lorenz– Krishnamurthy model of fast-slow interactions in the atmosphere. As is the case for many other twotime-scale systems, the various asymptotic procedures that may be used for this construction diverge, and there are no exactly invariant slow manifolds. Valuable information can however be gained by capturing the detail...

3-manifold Invariants from Cosets

We construct unitary modular categories for a general class of coset conformal field theories based on our previous study of these theories in the algebraic quantum field theory framework using subfactor theory. We also consider the calculations of the corresponding 3-manifold invariants. It is shown that under certain index conditions the link invaraints colored by the representations of coset...

On Witten’s 3-manifold Invariants

I distributed a preliminary version of some notes on Witten's recently discovered 3-manifold invariants. For various reasons the paper was never completed and published. Nevertheless, many people have told me that they still find the 1991 notes to be useful. For this reason, I have prepared this version of the notes which is distributable in electronic form. I have not attempted to correct, com...