Generic behavior of asymptotically holomorphic Lefschetz pencils.

We prove that the vanishing spheres of the Lefschetz pen- cils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplec- tomorphism group of the fiber. More precisely, a number of generalized Dehn twists may be used to conjugate those spheres. This implies the non-existence of homologically triv-ial vanishing spheres in these pencils. To develop the proof,we discuss some basic topological properties of the space of asymptotically holomorphic transverse sections.
CICYT
Research Training Network
Depto. de Álgebra, Geometría y Topología
Fac. de Ciencias Matemáticas
TRUE
pub