Bulletin of the
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Bull. Korean Math. Soc. 2012; 49(2): 435-443

Printed March 1, 2012

https://doi.org/10.4134/BKMS.2012.49.2.435

Copyright © The Korean Mathematical Society.

$T$-structure and the Yamabe invariant

Chanyoung Sung

Konkuk University

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 $T^m\times B$ where $T^m$ is the $m$-dimensional torus, and $B$ is a closed spin manifold with nonzero $\hat{A}$-genus has zero Yamabe invariant. We generalize this to various $T$-structured manifolds, for example $T^m$-bundles over such $B$ whose transition functions take values in $Sp(m,\Bbb Z)$ (or $Sp(m-1,\Bbb Z)\oplus \{\pm 1\}$ for odd $m$).

Keywords: Yamabe invariant, $T$-structure, torus bundle

MSC numbers: 53C20, 55R10

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