T-STRUCTURE AND THE YAMABE INVARIANT

Title & Authors
T-STRUCTURE AND THE YAMABE INVARIANT
Sung, Chan-Young;

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