T-structure and the Yamabe invariant

Details T-structure and the Yamabe invariant T-structure and the Yamabe invariant

2008-12-24

arxiv.org/abs/0812.4508v6

Mathematics

Differential Geometry

Scientific paper

The Yamabe invariant is an invariant of a closed smooth manifold, which contains information about possible scalar curvature on it. It is well-known that a product manifold T^m\times B where T^m$ is the m-dimensional torus, and B is a closed spin manifold of nonzero \hat{A}-genus has zero Yamabe invariant. We generalize it to various T-structured manifolds, for example T^m-bundles over such B whose transition functions take values in Sp(m,Z) (or Sp(m-1,Z)\oplus \pm 1 for odd m).

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