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$H$-Space structures on spaces of metrics of positive scalar curvature


Author: Georg Frenck
Journal: Trans. Amer. Math. Soc. 374 (2021), 8989-9006
MSC (2020): Primary 55P45, 58D17; Secondary 57R90
DOI: https://doi.org/10.1090/tran/8505
Published electronically: September 16, 2021
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct and study an $H$-space multiplication on ${\mathcal {R}}^+(M)$ for manifolds $M$ which are nullcobordant in their own tangential $2$-type. This is applied to give a rigidity criterion for the action of the diffeomorphism group on ${\mathcal {R}}^+(M)$ via pullback. We also compare this to other known multiplicative structures on ${\mathcal {R}}^+(M)$.


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References
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Additional Information

Georg Frenck
Affiliation: KIT, Karlsruher Institut für Technologie, Englerstraße 2, 76131 Karlsruhe, Bundesrepublik Deutschland
MR Author ID: 1430748
ORCID: 0000-0002-4260-7797
Email: math@frenck.net, georg.frenck@kit.edu

Received by editor(s): July 1, 2020
Received by editor(s) in revised form: May 17, 2021, and June 9, 2021
Published electronically: September 16, 2021
Additional Notes: The author was supported by the SFB 878 “Groups, Geometry and Actions”, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany ’s Excellence Strategy – EXC 2044 – 390685587, Mathematics Münster: Dynamics – Geometry - Structure and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 281869850 (RTG 2229)
Article copyright: © Copyright 2021 American Mathematical Society