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On the set of the logarithm of the LMO invariant for integral homology 3-spheres

Published online by Cambridge University Press:  01 September 2008

TOSHIE TAKATA
TOSHIE TAKATA*
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan. e-mail: takata@math.sc.niigata-u.ac.jp
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Abstract

The LMO invariant is a very strong invariant such that it is expected to classify integral homology 3-spheres. In this paper we identify the set of the degree ≤ 6 parts of the logarithm of the LMO invariant for integral homology 3-spheres. As an application, we obtain a complete set of relations which characterize the set of Ohtsuki's invariants {λi(M)} for i ≤ 6. For any simple Lie algebra , we also obtain a complete set of relations which characterize the set of perturbative P invariants {(M)} for i ≤ 3.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 2 , September 2008 , pp. 349 - 361
Copyright
Copyright © Cambridge Philosophical Society 2008

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