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Positive scalar curvature with symmetry

Research paper by Bernhard Hanke

Indexed on: 04 Dec '06Published on: 04 Dec '06Published in: Mathematics - Geometric Topology



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.