From mapping class groups to monoids of homology cobordisms: a survey

zbMath1291.57002arXiv1003.2512MaRDI QIDQ3144608

Kazuo Habiro, Gwénaël Massuyeau

Publication date: 8 December 2012

Full work available at URL: https://arxiv.org/abs/1003.2512

zbMATH Keywords

surveyTorelli groupJohnson homomorphismLMOhomology cylinders\(Y\)-filtrationhomology cobodismsMorita homomorphism

Mathematics Subject Classification ID

Related Items (19)

Abelian quotients of the \(Y\)-filtration on the homology cylinders via the LMO functor ⋮ An application of TQFT to modular representation theory ⋮ Triviality of the 𝐽₄-equivalence among homology 3-spheres ⋮ Torelli group, Johnson kernel, and invariants of homology spheres ⋮ A non-commutative Reidemeister-Turaev torsion of homology cylinders ⋮ Surgery equivalence relations for 3-manifolds ⋮ Tree homology and a conjecture of Levine ⋮ Abelian quotients of monoids of homology cylinders ⋮ Morita’s trace maps on the group of homology cobordisms ⋮ Alternative versions of the Johnson homomorphisms and the LMO functor ⋮ Homology cylinders of higher-order ⋮ Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism ⋮ Elliptic associators and the LMO functor ⋮ Johnson–Levine homomorphisms and the tree reduction of the LMO functor ⋮ A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces ⋮ An extension of the LMO functor ⋮ Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces ⋮ Equivalence relations for homology cylinders and the core of the Casson invariant ⋮ Geometric filtrations of string links and homology cylinders

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