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Abelian quotients of the
$Y$–filtration on the homology cylinders via the LMO
functor
Yuta Nozaki, Masatoshi Sato and Masaaki Suzuki |
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Geometry & Topology 26 (2022) 221–282
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DOI: 10.2140/gt.2022.26.221
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Abstract |
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We construct a series of homomorphisms from the –filtration on the monoid of homology cylinders to torsion modules via the mod reduction of the LMO functor. The restrictions of our homomorphisms to the lower central series of the Torelli group do not factor through Morita’s refinement of the Johnson homomorphism. We use it to show that the abelianization of the Johnson kernel of a closed surface has torsion elements. We also determine the third graded quotient of the –filtration. |
Keywords
Torelli group, Johnson kernel, homology cylinder, LMO
functor, clasper, Jacobi diagram, Johnson homomorphism,
Sato–Levine invariant
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Mathematical Subject Classification
Primary: 57K16, 57K20
Secondary: 57K31
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References |
Publication
Received: 9 February 2020
Revised: 24 September 2020
Accepted: 26 October 2020
Published: 5 April 2022
Proposed: Ciprian Manolescu
Seconded: Benson Farb, András I Stipsicz
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Authors |
| Yuta Nozaki | |
| Organization for the Strategic
Coordination of Research and Intellectual Properties Meiji University Tokyo Japan |
Graduate School of Advanced Science
and Engineering Hiroshima University Hiroshima Japan |
| Masatoshi Sato | |
| Department of Mathematics Tokyo Denki University Tokyo Japan |
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| Masaaki Suzuki | |
| Department of Frontier Media
Science Meiji University Tokyo Japan |
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