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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*
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan. e-mail: [email protected]

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2008

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