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2001 Positive scalar curvature, diffeomorphisms and the Seiberg–Witten invariants
Daniel Ruberman
Geom. Topol. 5(2): 895-924 (2001). DOI: 10.2140/gt.2001.5.895


We study the space of positive scalar curvature (psc) metrics on a 4–manifold, and give examples of simply connected manifolds for which it is disconnected. These examples imply that concordance of psc metrics does not imply isotopy of such metrics. This is demonstrated using a modification of the 1–parameter Seiberg–Witten invariants which we introduced in earlier work. The invariant shows that the diffeomorphism group of the underlying 4–manifold is disconnected. We also study the moduli space of positive scalar curvature metrics modulo diffeomorphism, and give examples to show that this space can be disconnected. The (non-orientable) 4–manifolds in this case are explicitly described, and the components in the moduli space are distinguished by a Pinc eta invariant.


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Daniel Ruberman. "Positive scalar curvature, diffeomorphisms and the Seiberg–Witten invariants." Geom. Topol. 5 (2) 895 - 924, 2001.


Received: 1 September 2001; Revised: 2 January 2002; Accepted: 31 December 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 1002.57064
MathSciNet: MR1874146
Digital Object Identifier: 10.2140/gt.2001.5.895

Primary: 57R57
Secondary: 53C21

Keywords: isotopy , positive scalar curvature , Seiberg–Witten equations

Rights: Copyright © 2001 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2001
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