Infinite loop spaces and positive scalar curvature

DOI10.1007/s00222-017-0719-3zbMath1377.53067arXiv1411.7408OpenAlexW1543390268MaRDI QIDQ2407543

Oscar Randal-Williams, Johannes Ebert, Boris Botvinnik

Publication date: 6 October 2017

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7408

zbMATH Keywords

Dirac operatorsspin manifoldcobordismreal \(K\)-theoryhomotopy equivalencehomotopy groupsPontrjagin-Thom construction(co)homologyHilbert bundlesMadsen-Tillmann-Weiss spectrumacyclic mapindex differencesurgery equivalencespinor bundlescollared boundaryquasifibrationspectrum map\(KR\)-theorysecondary index invariant(double) loop mapdouble torpedo metricLichnerowicz-Weitzenböck formulamaps weakly homotopicmoduli sapcesrelative index constructionspin Grassmannian

Mathematics Subject Classification ID

Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Index theory and related fixed-point theorems on manifolds (58J20) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Spin and Spin({}^c) geometry (53C27) Surgery and handlebodies (57R65) Other types of cobordism (57R90) Index theory (19K56) Infinite loop spaces (55P47) (Q)- and plus-constructions (19D06) Manifolds of metrics (especially Riemannian) (58D17)

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