2013/11/30 by Fabian Hebestreit, M. Joachim, Michael Joachim · 14 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cobordism #Combinatorics #Curvature #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Scalar (mathematics) #Scalar curvature #Spin (aerodynamics) #Topology (electrical circuits) #math.AT #math.DG #math.KT #msc:53C25 #msc:55N20 #msc:55N22 #msc:55P42 #msc:55R70
paper · pdf · doi:10.1112/topo.12122
published in Journal of Topology 13(1), 1-58 (Wiley) · 61 pages. Reworked exposition following a referee's report, to appear in Journal of Topology
arxiv created 2019/07/10 · openalex publication_date 2019/08/14 · arxiv updated 2019/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show how a suitably twisted spin cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others. We then investigate this parametrised spectrum, compute its m o d 2 -cohomology and generalise the Anderson–Brown–Peterson splitting of the usual spin cobordism spectrum to the twisted case. Along the way we also describe the m o d 2 -cohomology of various twisted, connective covers of real K-theory. In an Appendix we provide a comparison of our geometric models of twisted spin cobordism and twisted K-theory with others arising from abstract homotopy theory.