Monoids of moduli spaces of manifolds

DOI10.2140/gt.2010.14.1243zbMath1205.55007arXiv0905.2855OpenAlexW2099945683MaRDI QIDQ982161

Oscar Randal-Williams, Søren Galatius

Publication date: 6 July 2010

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

Full work available at URL: https://arxiv.org/abs/0905.2855

zbMATH Keywords

cobordism categorysurface bundlestopological monoids

Mathematics Subject Classification ID

Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Infinite loop spaces (55P47)

Related Items (19)

Homological stability for moduli spaces of high dimensional manifolds. II. ⋮ Book review of: B. Farb (ed.) et al., Moduli spaces of Riemann surfaces ⋮ The positive scalar curvature cobordism category ⋮ Stable homology of surface diffeomorphism groups made discrete ⋮ The space of short ropes and the classifying space of the space of long knots ⋮ Algebraic independence of generalized MMM-classes ⋮ Index theory in spaces of manifolds ⋮ The homotopy type of the topological cobordism category ⋮ The Picard group of the moduli space of \(r\)-spin Riemann surfaces ⋮ Mapping class groups of highly connected \((4k+2)\)-manifolds ⋮ A geometric interpretation of the homotopy groups of the cobordism category ⋮ The cohomology of Torelli groups is algebraic ⋮ Cohomology of automorphism groups of free groups with twisted coefficients ⋮ A note on the \((\infty,n)\)-category of cobordisms ⋮ Stable moduli spaces of high-dimensional manifolds ⋮ Cobordism categories and moduli spaces of odd dimensional manifolds ⋮ Spaces of graphs and surfaces: on the work of Søren Galatius ⋮ Semisimplicial spaces ⋮ Homological stability for spaces of embedded surfaces

Cites Work

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• The homotopy type of the cobordism category
• Stable homology of automorphism groups of free groups.
• Stability of the homology of the moduli spaces of Riemann surfaces with spin structure
• Stability of the homology of the mapping class groups of orientable surfaces
• Homology fibrations and the 'group-completion' theorem
• On the homotopy of the stable mapping class group
• The homology of the mapping class group
• Categories and cohomology theories
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• Homological stability for the mapping class groups of non-orientable surfaces
• A fibre bundle description of Teichmüller theory
• A vanishing theorem for characteristic classes of odd-dimensional manifold bundles
• An infinite loop space structure on the nerve of spin bordism categories

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