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Homotopy groups of the
moduli space of metrics of positive scalar curvature
Boris Botvinnik, Bernhard Hanke, Thomas Schick and Mark Walsh |
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Geometry & Topology 14 (2010) 2047–2076
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Abstract |
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We show by explicit examples that in many degrees in a stable range the homotopy groups of the moduli spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds can be non-trivial. This is achieved by further developing and then applying a family version of the surgery construction of Gromov–Lawson to certain nonlinear smooth sphere bundles constructed by Hatcher. |
Keywords
metrics of positive scalar curvature, moduli space of
positive scalar curvature metrics, classifying space of a
diffeomorphism group, Gromov–Lawson surgery parametrized by
a Morse function, rational homotopy type, Hatcher map
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Mathematical Subject Classification 2000
Primary: 53-02
Secondary: 55-02
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References |
Publication
Received: 30 July 2009
Revised: 19 October 2009
Accepted: 7 July 2010
Published: 29 August 2010
Proposed: Steve Ferry
Seconded: Ralph Cohen, Benson Farb
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Authors |
| Boris Botvinnik | |
| Department of Mathematics University of Oregon Eugene OR 97403 USA |
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| Bernhard Hanke | |
| Institut für Mathematik Universität Augsburg 86135 Augsburg Germany |
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| Thomas Schick | |
| Mathematisches Institut Georg-August-Universität Göttingen Bunsenstr. 3 37073 Göttingen Germany |
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| Mark Walsh | |
| Mathematisches Institut WWU Münster Einsteinstr. 62 48149 Münster Germany |
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