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Odd-dimensional solvmanifolds are contact

Christoph Bock

Abstract

Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold $Γ\backslash G$ is contact, where $Γ$ is a lattice in a connected and simply-connected solvable Lie group G of odd dimension.

Odd-dimensional solvmanifolds are contact

Abstract

Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold is contact, where is a lattice in a connected and simply-connected solvable Lie group G of odd dimension.

Paper Structure

This paper contains 4 theorems, 2 equations.

Key Result

Proposition 1

Let $M$ be an almost contact closed manifold. Then $M$ admits the structure of a contact manifold. ⁠ $\Box$

Theorems & Definitions (5)

  • Proposition 1
  • Theorem 2
  • Proposition 3
  • Remark
  • Theorem 4