Robert E. Gompf

Computer calculation of Witten's 3-manifold invariant

Wittens 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.

More Cappell-Shaneson spheres are standard

Akbulut has recently shown that an infinite family of Cappell‐Shaneson homotopy 4‐spheres is diffeomorphic to the standard 4‐sphere. In the present paper, a different method shows that a strictly larger family is standard. This new approach uses no Kirby calculus except through the relatively simple 1979 paper of Akbulut and Kirby showing that the simplest example with untwisted framing is standard. Instead, hidden symmetries of the original Cappell‐Shaneson construction are exploited. In the course of the proof, an example is given showing that Gluck twists can sometimes be undone using symmetries of fishtail neighborhoods. 57R60

Infinite order corks

We construct a compact, contractible 4-manifold

Spin c {structures and homotopy equivalences

C

Infinite order corks via handle diagrams

, an infinite-order self-diffeomorphism

Smooth embeddings with Stein surface images

f

Some well-disguised ribbon knots

of its boundary, and a smooth embedding of

On Cappell-Shaneson 4-spheres

C

Orbit spaces of gradient vector fields

into a closed, simply connected 4-manifold

Smooth 4-manifolds and Symplectic Topology

X