The positive scalar curvature cobordism category

DOI10.1215/00127094-2022-0023zbMath1502.53083arXiv1904.12951OpenAlexW2942536802MaRDI QIDQ2165744

Oscar Randal-Williams, Johannes Ebert

Publication date: 22 August 2022

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.12951

zbMATH Keywords

positive scalar curvaturecobordism categoriesdiffeomorphism groupsGromov-Lawson surgerysecondary index invariant

Mathematics Subject Classification ID

Exotic index theories on manifolds (58J22) Spin and Spin({}^c) geometry (53C27) Issues of holonomy in differential geometry (53C29) Other types of cobordism (57R90) Index theory (19K56) Infinite loop spaces (55P47) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (4)

Families of diffeomorphisms and concordances detected by trivalent graphs ⋮ Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds ⋮ Spaces of positive scalar curvature metrics on totally nonspin manifolds with spin boundary ⋮ Band width estimates via the Dirac operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(H\)-spaces, loop spaces and the space of positive scalar curvature metrics on the sphere
• The space of metrics of positive scalar curvature
• On the infinite loop space structure of the cobordism category
• The homotopy type of the cobordism category
• Quasifaserungen und unendliche symmetrische Produkte
• Algebraic topology
• Monoids of moduli spaces of manifolds
• Homotopy groups of the moduli space of metrics of positive scalar curvature
• Riemannian metrics of positive scalar curvature on compact manifolds with boundary
• The classification of simply connected manifolds of positive scalar curvature
• On the homotopy of the stable mapping class group
• Tori detect invertibility of topological field theories
• Categories and cohomology theories
• Infinite loop spaces and positive scalar curvature in the presence of a fundamental group
• Stable moduli spaces of high-dimensional manifolds
• The Gromov-Lawson-Chernysh surgery theorem
• The action of the mapping class group on metrics of positive scalar curvature
• Cobordism categories and moduli spaces of odd dimensional manifolds
• Semisimplicial spaces
• Infinite loop spaces and positive scalar curvature
• Index theory in spaces of manifolds
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• Finiteness conditions for CW-complexes. I, II.
• Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
• Metrics of positive scalar curvature and generalised Morse functions, part I
• On the Index of a Fibered Manifold
• Classifying spaces and fibrations
• Twisted spin cobordism and positive scalar curvature
• A quasifibration of spaces of positive scalar curvature metrics
• Fibering over the circle within a bordism class
• The stable mapping class group and \(Q(\mathbb C P^ \infty_ +)\).
• Codimension two index obstructions to positive scalar curvature

This page was built for publication: The positive scalar curvature cobordism category