Positive scalar curvature with symmetry

Details Positive scalar curvature with symmetry Positive scalar curvature with symmetry

2005-12-13

arxiv.org/abs/math/0512284v2

Mathematics

Geometric Topology

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

Scientific paper

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.

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