Finite type invariants of rational homology 3–spheres
نویسندگان
چکیده
منابع مشابه
On Finite Type 3-manifold Invariants V: Rational Homology 3-spheres
We introduce a notion of nite type invariants of oriented rational homology 3-spheres. We show that the map to nite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of nite type invari-ants of rational homology 3-spheres is a ltered commutative algebra with nite dimensional nonzero graded quotients only in degrees divisible by 3. We show that the Casson-Wal...
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Using elementary counting methods of weight systems for nite type invariants of knots and integral homology 3-spheres, in the spirit of B-NG], we answer positively three questions raised in Ga]. In particular, we exhibit a one-to-one map from the space of nite type invariants of integral homology 3-spheres to the space of nite type invariants of knots in S 3 .
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We are now embarrassingly rich in knot and 3-manifold invariants. We have to organize these invariants systematically and find out ways to make use of them. The theory of finite type knot invariants, or Vassiliev invariants, has been very successful in accomplishing the first task. Recently, an analogous theory of finite type invariants of integral homology 3-spheres started to emerge. The anal...
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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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...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2012
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2012.12.2389