Characteristic classes of surface bundles

DOI10.1007/BF01389178zbMath0608.57020OpenAlexW2089959701MaRDI QIDQ5903308

Shigeyuki Morita

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143521

zbMATH Keywords

mapping class groupclosed orientable surfacesurface bundlescharacteristic classes of surface bundlesgeneralized Nielsen realization problemsurface bundles with cross sections

Mathematics Subject Classification ID

Related Items (68)

On the homology groups of the mapping class groups of orientable surfaces with twisted coefficients ⋮ BNS INVARIANTS AND ALGEBRAIC FIBRATIONS OF GROUP EXTENSIONS ⋮ On the non-vanishing of the powers of the Euler class for mapping class groups ⋮ Some topological properties of surface bundles ⋮ Combinatorial Miller-Morita-Mumford classes and Witten cycles ⋮ Weil-Petersson volumes and cone surfaces ⋮ Homology of hyperelliptic mapping class groups for surfaces ⋮ Gribov problem, contact terms and Čech-De Rham cohomology in 2D topological gravity ⋮ Virtual Betti numbers and the symplectic Kodaira dimension of fibered $4$-manifolds ⋮ Stable homology of surface diffeomorphism groups made discrete ⋮ Families of Jacobian manifolds and characteristic classes of surface bundles. I ⋮ An integral Riemann-Roch theorem for surface bundles ⋮ Realization of the mapping class group by homeomorphisms ⋮ ON CLOSED LEAVES OF FOLIATIONS, MULTISECTIONS AND STABLE COMMUTATOR LENGTHS ⋮ Algebraic independence of generalized MMM-classes ⋮ The Meyer functions for projective varieties and their application to local signatures for fibered 4-manifolds ⋮ Integral Riemann–Roch formulae for cyclic subgroups of mapping class groups ⋮ Homomorphisms between mapping class groups ⋮ Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds ⋮ Moduli spaces of Riemann surfaces as Hurwitz spaces ⋮ Lagrangian mapping class groups from a group homological point of view ⋮ Abelianization and Nielsen realization problem of the mapping class group of a handlebody ⋮ A remark on the action of the mapping class group on the unit tangent bundle ⋮ Flat structures on surface bundles ⋮ Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra ⋮ On the moduli space of flat symplectic surface bundles ⋮ Periodicity for Mumford-Morita-Miller classes of surface symmetries ⋮ New results of intersection numbers on moduli spaces of curves ⋮ Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism ⋮ Improved homological stability for the mapping class group with integral or twisted coefficients ⋮ On Kodaira fibrations with invariant cohomology ⋮ Braid groups and discrete diffeomorphisms of the punctured disk ⋮ Characteristic classes of fiberwise branched surface bundles via arithmetic groups ⋮ Characteristic classes of Klein bottle bundles ⋮ Homological stability for the mapping class groups of non-orientable surfaces ⋮ Lectures on \(2\)D Yang-Mills theory, equivariant cohomology and topological field theories ⋮ On the background independence of two-dimensional topological gravity ⋮ The extension of Johnson's homomorphism from the Torelli group to the mapping class group ⋮ The Johnson homomorphism and the third rational cohomology group of the Torelli group ⋮ Periodic surface automorphisms and algebraic independence of Morita-Mumford classes ⋮ Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations ⋮ Characteristic classes via 4-dimensional gauge theory ⋮ Conformally invariant gauge fixed actions for 2-D topological gravity ⋮ Realization of the mapping class group of handlebody by diffeomorphisms ⋮ Geometric cycles and characteristic classes of manifold bundles (with an appendix by M. Krannich) ⋮ On the nonrealizability of braid groups by homeomorphisms ⋮ Families of Jacobian manifolds and characteristic classes of surface bundles. II ⋮ An infinite genus mapping class group and stable cohomology ⋮ Flat bundles and commutator lengths ⋮ Global fixed points for centralizers and Morita's theorem ⋮ On the non-realizability of braid groups by diffeomorphisms ⋮ Corrigendum: The diffeomorphism group of a K3 surface and Nielsen realization ⋮ A Glimpse into Thurston’s Work ⋮ Divisibility of the stable Miller-Morita-Mumford classes ⋮ Non‐realizability of the Torelli group as area‐preserving homeomorphisms ⋮ On the structure and the homology of the Torelli group ⋮ Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces ⋮ Characteristic classes of bundles of \(K3\) manifolds and the Nielsen realization problem ⋮ Riemann-Hurwitz formula for Morita-Mumford classes and surface symmetries ⋮ Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory ⋮ Equivalence relations for homology cylinders and the core of the Casson invariant ⋮ Analytic actions of mapping class groups on surfaces ⋮ \(E_2\)-cells and mapping class groups ⋮ Cohomological obstructions to Nielsen realization ⋮ Family of Jacobian manifolds and characteristic classes of surface bundles ⋮ On the homology of certain smooth covers of moduli spaces of algebraic curves ⋮ Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class groups ⋮ Characteristic classes of augmented bundles

Cites Work

• The second homology group of the mapping class group of an orientable surface
• Families of smooth curves
• Family of Jacobian manifolds and characteristic classes of surface bundles
• Stability of the homology of the mapping class groups of orientable surfaces
• The virtual cohomological dimension of the mapping class group of an orientable surface
• Family of Jacobian manifolds and characteristic classes of surface bundles. II
• Infinitesimal computations in topology
• The Euler characteristic of the moduli space of curves
• The homology of the mapping class group
• A certain type of irregular algebraic surfaces
• Teichmüller theory for surfaces with boundary
• The index of elliptic operators. IV, V
• Characteristic Classes and Homogeneous Spaces, I
• Foliations and groups of diffeomorphisms
• Characteristic Classes. (AM-76)
• The diffeomorphism group of a compact Riemann surface
• The Nielsen realization problem
• Characteristic classes of surface bundles

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