Monopoles and contact structures. (English) Zbl 0892.53015
The authors adapt the construction of the Seiberg-Witten invariants to the situation of a connected oriented 4-manifold \(X\) with nonempty boundary \(\partial X\) which is equipped with an oriented contact structure (an oriented field of 2-planes). Then two important results on symplectic forms on \(X\) due to C. H. Taubes [Math. Res. Lett. 1, 809-822 (1994; Zbl 0853.57019); ibid. 2, 9-13 (1995; Zbl 0854.57019)] are extended. A very delicate analysis for establishing the definitions and the properties of their invariants is done.
Reviewer: M.Anastasiei (Iaşi)
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 57R15 | Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) |
| 57N13 | Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) |
