Lagrangian mapping class groups from a group homological point of view

DOI10.2140/agt.2012.12.267zbMath1262.55006arXiv0910.5262OpenAlexW3103137681MaRDI QIDQ422096

Takuya Sakasai

Publication date: 16 May 2012

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.5262

zbMATH Keywords

mapping class groupTorelli groupLagrangian filtrationMiller-Morita-Mumford class

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Characteristic classes and numbers in differential topology (57R20) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Homology of classifying spaces and characteristic classes in algebraic topology (55R40)

Related Items (8)

Central extension of mapping class group via Chekhov-Fock quantization ⋮ Signature cocycles on the mapping class group and symplectic groups ⋮ Surface bundles over surfaces with arbitrarily many fiberings ⋮ The Meyer function on the handlebody group ⋮ Alternative versions of the Johnson homomorphisms and the LMO functor ⋮ Johnson–Levine homomorphisms and the tree reduction of the LMO functor ⋮ FINITE PRESENTATIONS OF CENTRALLY EXTENDED MAPPING CLASS GROUPS ⋮ \(E_2\)-cells and mapping class groups

Cites Work

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• Vanishing of universal characteristic classes for handlebody groups and boundary bundles
• The Picard group of the moduli space of curves with level structures
• Irreducible Sp-representations and subgroup distortion in the mapping class group
• On the homology of Lie groups made discrete
• A presentation for the special automorphism group of a free group
• The structure of the Torelli group. I: A finite set of generators for \({\mathcal I}\)
• A functorial LMO invariant for Lagrangian cobordisms
• 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 \({\mathcal S}\)
• The extension of Johnson's homomorphism from the Torelli group to the mapping class group
• The Schur multipliers of Sp\(_6(Z)\), Spin\(_8(Z)\), Spin\(_7(Z)\) and F\(_4(Z)\)
• The Schur multipliers of \(SL(3,Z)\) and \(SL(4,Z)\)
• The cohomology of \(SL_3(Z)\)
• An abelian quotient of the mapping class group \(\mathfrak S\)
• Finite type 3-manifold invariants, the mapping class group and blinks
• The cohomology ring of the colored braid group
• The Johnson homomorphism and the third rational cohomology group of the Torelli group
• Finite type invariants and fatgraphs
• A TQFT associated to the LMO invariant of three-dimensional manifolds
• The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres
• Calculating the image of the second Johnson-Morita representation
• Quadratic Forms and the Birman-Craggs Homomorphisms
• The μ-Invariant of 3-Manifolds and Certain Structural Properties of the Group of Homeomorphisms of a Closed, Oriented 2-Manifold
• The second homology groups of mapping class groups of orientable surfaces
• The diffeomorphism group of a compact Riemann surface
• Introduction to Algebraic K-Theory. (AM-72)
• Characteristic classes of surface bundles
• Homology cylinders: an enlargement of the mapping class group

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