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Positive scalar curvature with symmetry

Name: Positive scalar curvature with symmetry
Creator: Hanke, Bernhard
Keywords: Mathematics - Differential Geometry, Mathematics - Geometric Topology, primary 53C23, 53C25, 57R85; secondary 57R65, Differential Geometry (math.DG), secondary 57R65, primary 53C23, 53C25, 57R85, FOS: Mathematics, Geometric Topology (math.GT), 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2008Embargo end date: 01 Jan 2005 Germany Publisher:Walter de Gruyter GmbHJournal:Journal für die reine und angewandte Mathematik (Crelles Journal), volume 2,008 (issn: 0075-4102, eissn: 1435-5345,

Authors: Hanke, Bernhard;

doi: 10.1515/crelle.2008.003 , 10.48550/arxiv.math/0512284

arXiv: http://arxiv.org/abs/math/0512284

Positive scalar curvature with symmetry

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Abstract

We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension-2 surgery technique which removes singular strata from fixed point free $S^1$-manifolds while preserving equivariant positive scalar curvature. These results are applied to derive the following generalization of a result of Gromov and Lawson: Each closed fixed point free $S^1$-manifold of dimension at least 6 whose isotropy groups have odd order and whose union of maximal orbits is simply connected and not spin carries an $S^1$-invariant metric of positive scalar curvature.

36 pages, 1 figure, minor changes; to appear in J. Reine Angew. Math

Country

Germany

Related Organizations

University of Augsburg
Germany

Keywords

Mathematics - Differential Geometry, Mathematics - Geometric Topology, primary 53C23, 53C25, 57R85; secondary 57R65, Differential Geometry (math.DG), secondary 57R65, primary 53C23, 53C25, 57R85, FOS: Mathematics, Geometric Topology (math.GT)

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