Twisted spin cobordism and positive scalar curvature. Issue 1 (14th August 2019)

• Record Type: Journal Article
• Authors: Hebestreit, Fabian; Joachim, Michael
• Is Part Of: Journal of topology. Volume 13:Issue 1(2020)
• Page Start: 1
• Page End: 58
• Publication Date: 2019-08-14
• Subjects: 55N22 (primary) -- 55R70 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12122
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: 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.