Seiberg-Witten invariants of rational homology 3-spheres. Part I
نویسنده
چکیده
2 Seiberg-Witten invariants of closed 3-manifolds 9 2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 The case b1 > 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 The case b1 = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 The case b1 = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
منابع مشابه
Seiberg Witten Invariants of Rational Homology 3-spheres
In 1996 Meng and Taubes [16] have established a relationship between the Seiberg– Witten invariants of a (closed) 3-manifold with b1 > 0 and the Milnor torsion. A bit later Turaev, [29, 30], enhanced Meng–Taubes’ result, essentially identifying the Seiberg–Witten invariant with the refined torsion he introduced earlier in [27]. In [29] Turaev raised the question of establishing a connection bet...
متن کاملSurgery Formula for Seiberg–witten Invariants of Negative Definite Plumbed 3-manifolds
We derive a cut-and-paste surgery formula of Seiberg–Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma’s recursion formula [27, 4.5] targeting analytic invariants of splice-quotient singularities. Combining the two formulas automatically provides a proof of the equivariant version [11, 5.2(b)] of the Seiberg–Witten invariant c...
متن کاملSeiberg-Witten-Floer Theory for Homology 3-Spheres
We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant is defined taking values in the Seiberg-Witten-Floer homology group, these relative Seiberg-Witten invariants are applied to certain homology spheres boundin...
متن کاملVariants of Equivariant Seiberg-Witten Floer Homology
For a rational homology 3-sphere Y with a Spin structure s, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology in [5] lead to a collection of variants HF ∗,U(1)(Y, s), HF SW,∞ ∗,U(1) (Y, s) HF SW,+ ∗,U(1)(Y, s), ĤF SW ∗ (Y, s) and HF SW red,∗(Y, s) which are topological invariants. We establish a long exact sequence relating HF ∗,U(1)(Y,...
متن کاملOn the Ozsváth–Szabó invariant of negative definite plumbed 3–manifolds
The main goal of the present article is the computation of the Heegaard Floer homology introduced by Ozsváth and Szabó for a family of plumbed rational homology 3–spheres. The main motivation is the study of the Seiberg–Witten type invariants of links of normal surface singularities. AMS Classification numbers Primary: 57M27, 57R57 Secondary: 14E15, 14B15, 14J17, 32S25, 32S45
متن کامل