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

Toshie Takata

doi:10.1017/S030500410800145X

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

Toshie Takata

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 {λ_i(M)} for i ≤ 6. For any simple Lie algebra g, we also obtain a complete set of relations which characterize the set of perturbative Pg invariants {λ _i^g(M)} for i ≤ 3.

Original language	English
Pages (from-to)	349-361
Number of pages	13
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	145
Issue number	2
DOIs	https://doi.org/10.1017/S030500410800145X
Publication status	Published - Sept 1 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1017/S030500410800145X

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AB - 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 g, we also obtain a complete set of relations which characterize the set of perturbative Pg invariants {λ ig(M)} for i ≤ 3.

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

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