Lefschetz fibrations on adjoint orbits

Abstract

We prove that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We then describe the topology of the regular and singular fibres, in particular calculating their middle Betti numbers. For the example of sl(2,C) we compute the Fukaya--Seidel category of Lagrangian vanishing cycles.

Final Version in Forum Mathematicum 2015

References in corpus (1)

• Adjoint orbits of semi-simple Lie groups and Lagrangean submanifolds

Cited by in corpus (3)

• Adjoint orbits of semi-simple Lie groups and Lagrangean submanifolds
• Hodge Diamonds and Adjoint Orbits
• Symplectic Lefschetz Fibrations from a Lie-theoretical Viewpoint