Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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T-STRUCTURE AND THE YAMABE INVARIANT

  • Sung, Chan-Young (Department of Mathematics and Institute for Mathematical Sciences Konkuk University)
  • Received : 2010.12.23
  • Published : 2012.03.31
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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 $\^{A}$-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, $\mathbb{Z}$) (or Sp(m - 1, $\mathbb{Z}$) ${\oplus}\;{{\pm}1}$ for odd m).

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