3,702 research outputs found
Lagrangian submanifolds and Lefschetz pencils
Given a Lagrangian submanifold in a symplectic manifold and a Morse function
on the submanifold, we show that there is an isotopic Morse function and a
symplectic Lefschetz pencil on the manifold extending the Morse function to the
whole manifold. From this construction we define a sequence of symplectic
invariants classifying the isotopy classes of Lagrangian spheres in a
symplectic 4-manifold.Comment: 40 pages, 1 figur
On fibered commensurability
This paper initiates a systematic study of the relation of commensurability
of surface automorphisms, or equivalently, fibered commensurability of
3-manifolds fibering over the circle. We show that every hyperbolic fibered
commensurability class contains a unique minimal element, whereas the class of
Seifert manifolds fibering over the circle consists of a single
commensurability class with infinitely many minimal elements. The situation for
non-geometric manifolds is more complicated, and we illustrate a range of
phenomena that can occur in this context.Comment: 26 pages, 16 figures; version 2 incorporates referee's comment
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