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Presentation
Hard Leschetz Theorem for K-contact Manifolds
Gone fishing Poisson meeting” (2014)
  • Yi Lin
Abstract

Recently, Cappelletti-Montano, De Nicola, and Yudin proved a Hard Lefschetz theorem for the De Rham cohomology of compact Sasakian manifolds, and proposed an associated notion of Lefschetz contact manifolds. In this talk, we discuss a new approach to the Hard Lefschetz theorem for Sasakian manifolds using the formalism of odd dimensional symplectic geometry. This leads to a more general Hard Lefschetz theorem for K-contact manifolds, and provides us a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a Lefschetz contact five manifolds. As an application, we show how to use our methods to construct simply-connected K-contact manifolds which do not support any Sasakian structures. This in particular answers an open question asked by Boyer and late Galicki.

Keywords
  • Cappelletti-Montano,
  • De Nicola,
  • Yudin,
  • Hard Lefschetz theorem,
  • De Rham cohomology,
  • Sasakian manifolds,
  • K-contact manifolds
Disciplines
Publication Date
November, 2014
Citation Information
Yi Lin. "Hard Leschetz Theorem for K-contact Manifolds" Gone fishing Poisson meeting” (2014)
Available at: http://works.bepress.com/yi_lin/12/