On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions

2003/12/03 by Hui Li, Li, Hui
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.SG #msc:53D05 #msc:53D20

paper · pdf · doi:10.48550/arxiv.math/0312085

15 pages

arxiv created 2003/12/03 · arxiv updated 2009/12/01

Abstract

Let (M, ω) be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian S¹ action such that the fixed point set consists of isolated points or surfaces. Assume dim H²(M)<3, in \citeL, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six ``types''. In this paper, we construct such manifolds with these ``types''. As a consequence, we have a precise list of the values of these invariants.

Related

• Semi-free Hamiltonian circle actions on 6 dimensional symplectic manifolds
• Hamiltonian S¹ actions with Isolated Fixed Points on 6-Dimensional Symplectic Manifolds
• Non-Hamiltonian actions with isolated fixed points
• Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I
• Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions III