Stable moduli spaces of high-dimensional manifolds

DOI10.1007/s11511-014-0112-7zbMath1377.55012arXiv1201.3527OpenAlexW2090195727MaRDI QIDQ2015963

Oscar Randal-Williams, Søren Galatius

Publication date: 18 June 2014

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3527

zbMATH Keywords

stabilizationmoduli spacecharacteristic classesinfinite loop spacefiber bundles

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Surgery and handlebodies (57R65) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Other types of cobordism (57R90) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Infinite loop spaces (55P47) Differential topological aspects of diffeomorphisms (57R50)

Related Items (48)

The action of the mapping class group on metrics of positive scalar curvature ⋮ Homological stability for moduli spaces of high dimensional manifolds. II. ⋮ Characteristic classes for families of bundles ⋮ Abelian quotients of mapping class groups of highly connected manifolds ⋮ The positive scalar curvature cobordism category ⋮ Homological stability for automorphism groups ⋮ An upper bound for the pseudoisotopy stable range ⋮ Stable homology of surface diffeomorphism groups made discrete ⋮ Infinite loop spaces and positive scalar curvature ⋮ Homological stability and stable moduli of flat manifold bundles ⋮ Operations on stable moduli spaces ⋮ Homological stability for moduli spaces of high dimensional manifolds. I ⋮ Tautological classes of definite 4-manifolds ⋮ Simplicial volume and essentiality of manifolds fibered over spheres ⋮ ON THE COHOMOLOGY OF TORELLI GROUPS ⋮ Diffeomorphisms of discs ⋮ Homological stability: a tool for computations ⋮ Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds ⋮ Finiteness properties of automorphism spaces of manifolds with finite fundamental group ⋮ Homology stability for symmetric diffeomorphism and mapping class groups ⋮ The stable cohomology of self-equivalences of connected sums of products of spheres ⋮ On the moduli space of flat symplectic surface bundles ⋮ Generalised Miller-Morita-Mumford classes for block bundles and topological bundles ⋮ A geometric interpretation of the homotopy groups of the cobordism category ⋮ On characteristic classes of exotic manifold bundles ⋮ Characteristic numbers of manifold bundles over surfaces with highly connected fibers ⋮ On the topology of the space of Ricci-positive metrics ⋮ Spaces of positive intermediate curvature metrics ⋮ Homological stability for moduli spaces of disconnected submanifolds. I ⋮ Infinite loop spaces and positive scalar curvature in the presence of a fundamental group ⋮ The space of positive scalar curvature metrics on a manifold with boundary ⋮ Torelli spaces of high-dimensional manifolds ⋮ The Gromov-Lawson-Chernysh surgery theorem ⋮ A vanishing theorem for tautological classes of aspherical manifolds ⋮ Homological stability for the moduli spaces of products of spheres ⋮ On the Farrell-Jones conjecture for Waldhausen's \(A\)-theory ⋮ Geometric cycles and characteristic classes of manifold bundles (with an appendix by M. Krannich) ⋮ On rational homological stability for block automorphisms of connected sums of products of spheres ⋮ Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+ 1 ⋮ Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers ⋮ Cobordism categories and moduli spaces of odd dimensional manifolds ⋮ Some hermitian K-groups via geometric topology ⋮ Rational Pontryagin classes of Euclidean fiber bundles ⋮ Dynamical and cohomological obstructions to extending group actions ⋮ Semisimplicial spaces ⋮ Some finiteness results for groups of automorphisms of manifolds ⋮ Homological stability for spaces of embedded surfaces ⋮ Relations among characteristic classes of manifold bundles

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