Scott Baldridge

SEIBERG–WITTEN INVARIANTS OF 4-MANIFOLDS WITH FREE CIRCLE ACTIONS

The main results of this paper describes a formula for the Seiberg–Witten invariant of a 4-manifold which admits a nontrivial free circle action. We use this theorem to produce a nonsymplectic 4-manifold with a free circle action whose orbit space fibers over circle. We also describe a nontrivial 3-manifold which is not the orbit space of any symplectic 4-manifold with a free circle action. A corollary of the main theorem is a formula for the 3-dimensional Seiberg–Witten invariants of the total space of a circle bundle over a surface.

Seiberg-Witten invariants, orbifolds, and circle actions

The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point-free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the moduli space of the 4-manifold and the moduli space of the quotient 3-orbifold. Two corollaries include the fact that b + >1 4-manifolds with fixed-point-free circle actions are simple type and a new proof of the equality SW Y 3 × S 1 = SW Y 3. An infinite number of 4-manifolds with b + = 1 whose Seiberg-Witten invariants are still diffeomorphism invariants is constructed and studied.

On symplectic 4-manifolds with prescribed fundamental group

In this article we study the problem of minimizing a? + bs on the class of all symplectic 4-manifolds with prescribed fundamental group G (? is the Euler characteristic, s is the signature, and a,?b ? R), focusing on the important cases ?, ? + s and 2? + 3s. In certain situations we can derive lower bounds for these functions and describe symplectic 4-manifolds which are minimizers. We derive an upper bound for the minimum of ? and ? + s in terms of the presentation of G.

Simply connected minimal symplectic 4-manifolds with signature less than - 1

For each pair

Geography of symplectic 4-manifolds with Kodaira dimension one

(e,\sigma)

CUBE DIAGRAMS AND 3-DIMENSIONAL REIDEMEISTER-LIKE MOVES FOR KNOTS

of integers satisfying

Seiberg--Witten vanishing theorem for S1-manifolds with fixed points

2e+3\sigma\ge 0

Constructions of small symplectic 4-manifolds using Luttinger surgery

,

Elementary Mathematics for Teachers

\sigma\leq -2

A symplectic manifold homeomorphic but not diffeomorphic to CP2#3CP2

, and