The homotopy type of the topological cobordism category

DOI10.25537/dm.2022v27.2107-2182MaRDI QIDQ2695703

Mauricio Gomez Lopez, Alexander Kupers

Publication date: 3 April 2023

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

Full work available at URL: https://arxiv.org/abs/1810.05277

zbMATH Keywords

cobordism categoriestopological manifolds

Mathematics Subject Classification ID

Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Cobordism and concordance in topological manifolds (57N70)

Cites Work

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• Simplicial principal bundles in parametrized spaces
• The homotopy type of the cobordism category
• Monoids of moduli spaces of manifolds
• Groups of automorphisms of manifolds. With an appendix by E. Peders en
• Embedding spaces
• Piecewise linear embeddings of manifolds
• Categories and cohomology theories
• An additivity theorem for cobordism categories
• Three applications of delooping to \(h\)-principles
• Semisimplicial spaces
• Microbundles
• Microbundles are fibre bundles
• Piecewise linear bundles in the stable range
• Classifying spaces and spectral sequences
• Smoothing 4-manifolds
• Deformation of homeomorphisms on stratified sets
• Quasi-topologies
• Embedded Cobordism Categories and Spaces of Submanifolds
• On Spaces Having the Homotopy Type of a CW-Complex
• Topological manifold bundles and the 𝐴-theory assembly map
• Partial Differential Relations
• Topological transversality holds in all dimensions
• The homotopy type of the space of diffeomorphisms. I
• Characteristic Classes. (AM-76)
• Piecewise Linear Bundles in the Metastable Range
• General Position Maps for Topological Manifolds in the 2/3RDS Range
• Classifying spaces and fibrations
• Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
• Cobordism categories of manifolds with corners
• Microbundles and bundles
• Normal Structures for Locally Flat Embeddings
• On the Haefliger knot groups