Torelli group, Johnson kernel, and invariants of homology spheres

DOI10.4171/QT/138zbMath1462.57017arXiv1711.07855MaRDI QIDQ2192434

Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai

Publication date: 17 August 2020

Published in: Quantum Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.07855

zbMATH Keywords

Casson invariantfinite type invariantlower central seriesTorelli groupJohnson filtrationJohnson kernelhomology 3-sphereOhtsuki invariant

Mathematics Subject Classification ID

Cohomology of Lie (super)algebras (17B56) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Derived series, central series, and generalizations for groups (20F14) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (7)

On finite generation of the Johnson filtrations ⋮ Abelian quotients of the \(Y\)-filtration on the homology cylinders via the LMO functor ⋮ Effective finite generation for \([\mathrm{IA}_n,\mathrm{IA}_n\) and the Johnson kernel] ⋮ On the kernel of the surgery map restricted to the 1‐loop part ⋮ On the Torelli Lie algebra ⋮ Surgery equivalence relations for 3-manifolds ⋮ Unnamed Item

Cites Work

• Unnamed Item
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• The structure of the Torelli group. II: A characterization of the group generated by twists on bounding curves
• The structure of the Torelli group. III: The abelianization of \({\mathcal S}\)
• Casson's invariant for homology 3-spheres and characteristic classes of surface bundles
• On the structure of the Torelli group and the Casson invariant
• An abelian quotient of the mapping class group \(\mathfrak S\)
• Abelian quotients of subgroups of the mapping class group of surfaces
• Finite type 3-manifold invariants and the structure of the Torelli group. I
• On finiteness properties of the Johnson filtrations
• The Johnson homomorphism and the third rational cohomology group of the Torelli group
• Casson's invariant for homology 3-spheres and characteristic classes of surface bundles. I
• A polynomial invariant of rational homology \(3\)-spheres
• Arithmetic group symmetry and finiteness properties of Torelli groups
• Computations in formal symplectic geometry and characteristic classes of moduli spaces
• The abelianization of the Johnson kernel
• Bordism invariants of the mapping class group
• Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras
• Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant
• From mapping class groups to monoids of homology cobordisms: a survey
• A survey of the Torelli group
• The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres
• Integral homology $3$-spheres and the Johnson filtration
• The μ-Invariant of 3-Manifolds and Certain Structural Properties of the Group of Homeomorphisms of a Closed, Oriented 2-Manifold
• Infinitesimal presentations of the Torelli groups
• FINITE TYPE INVARIANTS OF INTEGRAL HOMOLOGY 3-SPHERES
• Links, pictures and the homology of nilpotent groups

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