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A symplectic manifold homeomorphic but not diffeomorphic to CP2#3CP2
In this paper we construct a minimal symplectic 4-manifold and prove it is homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)
Constructions of small symplectic 4-manifolds using Luttinger surgery
In this article we use the technique of Luttinger surgery to produce small examples of simply connected and non-simply connected minimal symplectic 4-manifolds. In particular, we construct: (1) AnExpand
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 theExpand
Simply connected minimal symplectic 4-manifolds with signature less than --1
For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$, $\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplecticExpand
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 nonsymplecticExpand
Symplectic 4-manifolds with arbitrary fundamental group near the Bogomolov--Miyaoka--Yau line
In this paper we construct a family of symplectic 4--manifolds with positive signature for any given fundamental group $G$ that approaches the BMY line. The family is used to show that one cannotExpand
Cube diagrams and a homology theory for knots
In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under twoExpand
Seiberg--Witten vanishing theorem for S1-manifolds with fixed points
We show that the Seiberg-Witten invariant is zero for all smooth 4-manifolds with b + >1 that admit circle actions having at least one fixed point. We also show that all symplectic 4-manifolds thatExpand
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,?bExpand