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On Finite Type 3-Manifold Invariants V: Rational Homology 3-Spheres (1995)
| Citations: | 6 - 2 self |
BibTeX
@MISC{Garoufalidis95onfinite,
author = {Stavros Garoufalidis and Tomotada Ohtsuki},
title = {On Finite Type 3-Manifold Invariants V: Rational Homology 3-Spheres},
year = {1995}
}
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Abstract
. We introduce a notion of finite type invariants of oriented rational homology 3-spheres. We show that the map to finite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of finite type invariants of rational homology 3-spheres is a filtered commutative algebra with finite dimensional nonzero graded quotients only in degrees divisible by 3. We show that the Casson-Walker invariant is of type 3. We mention an alternative B-finite-type notion of invariants of rational homology 3-spheres, with "better grading" properties, and show that type 3m invariants of rational homology 3-spheres are included in B-type m invariants. Finally, we prove a nonexistence theorem for finite type invariants of oriented, closed 3-manifolds. Contents 1. Introduction 2 1.1. Motivation 1.2. Statement of the results 1.3. Questions 1.4. Plan of the proof 1.5. A philosophical comment 1.6. Acknowledgment 2. Exceptional Dehn surgeries 7 The first named author was...
Keyphrases
rational homology 3-spheres finite type 3-manifold invariant finite type invariant casson-walker invariant integral homology 3-spheres type invariant finite dimensional nonzero b-type invariant filtered commutative algebra oriented rational homology 3-spheres exceptional dehn nonexistence theorem alternative b-finite-type notion philosophical comment
