Mapping class group and the Casson invariant
نویسندگان
چکیده
منابع مشابه
On the Casson Knot Invariant
In our previous paper 19] we introduced a new type of combinatorial formulas for Vassiliev knot invariants and presented lots of formulas of this type. To the best of our knowledge, these formulas are by far the simplest and the most practical for computational purposes. Since then Goussarov has proved the main conjecture formulated in 19]: any Vassiliev knot invariant can be described by such ...
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The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that may allow for more effective invariants. Finally it is shown how the dimensional reduction of these theories corresponds to a generalization of the topologica...
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We bound the value of the Casson invariant of any integral homology 3-sphere M by a constant times the distance-squared to the identity, measured in any word metric on the Torelli group I, of the element of I associated to any Heegaard splitting of M . We construct examples which show this bound is asymptotically sharp.
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We derive formulae which lend themselves to TQFT interpretations of the Milnor torsion, the Lescop invariant, the Casson invariant, and the Casson-Morita cocyle of a 3-manifold, and, furthermore, relate them to the Reshetikhin-Turaev theory. AMS Classification 57R56, 57M27; 17B10, 17B37, 17B50, 20C20
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We use Heegaard decompositions and the theta divisor on a Riemann-ian surface to define a three-manifold invariant for rational homology three-spheres. This invariant is defined on the set of Spin c structures θ : Spin c (Y) −→ Q. In the first part of the paper, we give the definition of the invariant (which builds on the theory developed in [18]). In the second part, we establish a relationshi...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2004
ISSN: 0373-0956
DOI: 10.5802/aif.2045