Stability of the homology of the mapping class groups of orientable surfaces

DOI10.2307/1971172zbMath0579.57005OpenAlexW2047753277MaRDI QIDQ1067257

John L. Harer

Publication date: 1985

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1971172

zbMATH Keywords

group of orientation preserving diffeomorphismshomology groups of the mapping class group of a surfacesurface of genus g with r boundary componentsThurston's lamination space

Mathematics Subject Classification ID

Related Items (only showing first 100 items - show all)

Embedded spheres in \(S^2 \times S^1\# \cdots \# S^2 \times S^1\) ⋮ On the homology groups of the mapping class groups of orientable surfaces with twisted coefficients ⋮ The homology of the Brauer algebras ⋮ On the non-vanishing of the powers of the Euler class for mapping class groups ⋮ Combinatorial Miller-Morita-Mumford classes and Witten cycles ⋮ Automorphisms of free groups with boundaries. ⋮ Unnamed Item ⋮ Mapping class groups and outer automorphism groups of free groups are \(C^{*}\)-simple ⋮ Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields ⋮ Hierarchical hyperbolicity of graphs of multicurves ⋮ Book review of: B. Farb (ed.) et al., Moduli spaces of Riemann surfaces ⋮ Commensurations of the Johnson kernel ⋮ Stable cohomology of the perfect cone toroidal compactification of \(\mathcal{A}_g\) ⋮ Connectivity of complexes of separating curves ⋮ A homology-valued invariant for trivalent fatgraph spines ⋮ Tethers and homology stability for surfaces ⋮ Homological stability for automorphism groups ⋮ Stable homology of surface diffeomorphism groups made discrete ⋮ Borel stability for congruence subgroups ⋮ The hyperbolicity of the sphere complex via surgery paths ⋮ Splittings of free groups, normal forms and partitions of ends ⋮ Homological stability for diffeomorphism groups of high-dimensional handlebodies ⋮ Infinite loop spaces from operads with homological stability ⋮ Closed/open string diagrammatics ⋮ The high-dimensional cohomology of the moduli space of curves with level structures ⋮ On the edge of the stable range ⋮ Operations on stable moduli spaces ⋮ Topological methods in moduli theory ⋮ Asymptotically rigid mapping class groups. I: Finiteness properties of braided Thompson's and Houghton's groups ⋮ Stabilization for mapping class groups of 3-manifolds ⋮ The homotopy type of the cobordism category ⋮ A heuristic for the distribution of point counts for random curves over a finite field ⋮ Hochschild homology of structured algebras ⋮ Geometry and rigidity of mapping class groups. ⋮ Madsen-Weiss for geometrically minded topologists ⋮ The structure of 2D semi-simple field theories ⋮ Derived localisation of algebras and modules ⋮ Towards representation stability for the second homology of the Torelli group. ⋮ Stable homology of automorphism groups of free groups. ⋮ The complex of partial bases for \(F_n\) and finite generation of the Torelli subgroup of \(\Aut(F_n)\). ⋮ Homology of the curve complex and the Steinberg module of the mapping class group ⋮ On the moduli space of flat symplectic surface bundles ⋮ An arc graph distance formula for the flip graph ⋮ Relations among tautological classes revisited ⋮ Contractible, hyperbolic but non-CAT(0) complexes ⋮ Hyperbolicity of the complex of free factors. ⋮ Laurent phenomenon algebras arising from surfaces. II: Laminated surfaces ⋮ Realisation and dismantlability ⋮ The second rational homology group of the moduli space of curves with level structures ⋮ The first homology group of the mapping class group of a nonorientable surface with twisted coefficients ⋮ Representation stability for the cohomology of the moduli space \(\mathcal M_{g}^{n}\) ⋮ On characteristic classes of exotic manifold bundles ⋮ Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018 ⋮ Improved homological stability for the mapping class group with integral or twisted coefficients ⋮ Moduli space actions on the Hochschild co-chains of a Frobenius algebra. II: Correlators ⋮ Braids, mapping class groups, and categorical delooping ⋮ On the cohomology of pure mapping class groups as FI-modules ⋮ Cutting and pasting in the Torelli group ⋮ Homological stability for moduli spaces of disconnected submanifolds. I ⋮ Flat surfaces and stability structures ⋮ A second cohomology class of the symplectomorphism group with the discrete topology ⋮ Moduli space actions on the Hochschild co-chains of a Frobenius algebra. I: Cell operads ⋮ \(E_n\)-cell attachments and a local-to-global principle for homological stability ⋮ Homological stability for the mapping class groups of non-orientable surfaces ⋮ Connectedness of curve complex of surface ⋮ Monoids of moduli spaces of manifolds ⋮ On the ideal triangulation graph of a punctured surface ⋮ The third homology group of the moduli space of curves ⋮ Geometric cycles and characteristic classes of manifold bundles (with an appendix by M. Krannich) ⋮ Moduli spaces and macromolecules ⋮ The fibres of the Scott map on polygon tilings are the flip equivalence classes ⋮ Cluster algebras and triangulated surfaces. I: Cluster complexes ⋮ Spaces of commuting elements in the classical groups ⋮ Fundamental groups of moduli stacks of stable curves of compact type ⋮ A class function on the mapping class group of an orientable surface and the Meyer cocycle ⋮ On the Farrell cohomology of mapping class groups ⋮ Big Mapping Class Groups: An Overview ⋮ Canonical extensions of the Johnson homomorphisms to the Torelli groupoid ⋮ Bounded cohomology of subgroups of mapping class groups ⋮ Stability of the homology of the moduli spaces of Riemann surfaces with spin structure ⋮ ABELIAN COVERS OF SURFACES AND THE HOMOLOGY OF THE LEVEL L MAPPING CLASS GROUP ⋮ The Euler characteristic of the moduli space of curves ⋮ Torsion in the mapping class group and its cohomology ⋮ An application of homotopy theory to mapping class groups ⋮ An infinite presentation of the Torelli group ⋮ Spaces of graphs and surfaces: on the work of Søren Galatius ⋮ Higher finiteness properties of braided groups ⋮ Homeomorphic subsurfaces and the omnipresent arcs ⋮ Riemann-Hurwitz formula for Morita-Mumford classes and surface symmetries ⋮ Matrix group integrals, surfaces, and mapping class groups. I. \(\mathrm{U}(\mathrm{n})\) ⋮ Relations in the tautological ring of \({\mathcal M}_g\) ⋮ Sections of surface bundles and Lefschetz fibrations ⋮ Homological stability of topological moduli spaces ⋮ \(E_2\)-cells and mapping class groups ⋮ THE CO-HOPFIAN PROPERTY OF SURFACE BRAID GROUPS ⋮ On triangulations of surfaces ⋮ On the homology of certain smooth covers of moduli spaces of algebraic curves ⋮ Retraction of: ``Linear representations of hyperelliptic mapping class groups ⋮ Homological stability for spaces of embedded surfaces ⋮ Relations among characteristic classes of manifold bundles

This page was built for publication: Stability of the homology of the mapping class groups of orientable surfaces