T-structure and the Yamabe invariant

2008/12/24 by Sung, Chanyoung
#53C20 #55R10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0812.4508

Abstract

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× B where T^m is the m-dimensional torus, and B is a closed spin manifold of nonzero 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)⊕ ± 1 for odd m).

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