The Seiberg–Witten invariants and 4–manifolds with essential tori

By Clifford H. Taubes. 2001

61 citations recorded by the source corpus.

A formula is given for the Seiberg{Witten invariants of a 4{manifold that is cut along certain kinds of 3{dimensional tori. The formula involves a Seiberg{ Witten invariant for each of the resulting pieces. AMS Classication numbers Primary: 57R57 Secondary: 57M25, 57N13

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/574e775a0db8d8274faa4882cadb45750aeec07f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Michael Hutchings
2. Daniel Cristofaro-Gardiner
3. D. Mcduff
4. Jean Gutt
5. F. Schlenk
6. Clifford H. Taubes

In Discrete Mathematics and Combinatorics

1. Michael Hutchings
2. Clifford H. Taubes
3. Andrew Cotton-Clay
4. Richard Siefring
5. Daniel Cristofaro-Gardiner
6. P. Seidel
7. I. Smith
8. F. Schlenk

In Geometry and Topology

1. Michael Hutchings
2. Daniel Cristofaro-Gardiner
3. Richard Siefring
4. Clifford H. Taubes
5. Andrew Cotton-Clay
6. F. Schlenk
7. D. Mcduff
8. Michael C. Sullivan

Citations in the corpus

• Families of simply connected 4-manifolds with the same Seiberg-Witten invariants (2002, unknown): “which is represented by the torus S1 1 × {point in a1} × ∂D2 on ∂(Z′ \(Λ(a1)×D2)) = ∂(Z′ \(S1 1 ×a1 ×D2)). Since Λ(a1) is nullhomologous, the surgery formula of Morgan, Mrowka, Szabo [MMS] and Taubes [T3] (see also [FS2]) states SWZ′(m)(ζ) = SWZ′(ζ) −m X i,j SWZˆ′(ζ +jτ). For each basic class k of X”
• An index inequality for embedded pseudoholomorphic curves in symplectizations (2001, result): “Analogues of our results should also hold in three dimensional contact topology.”