Monodromy groups of Lagrangian tori in the symplectic 4-space

Details Monodromy groups of Lagrangian tori in the symplectic 4-space Monodromy groups of Lagrangian tori in the symplectic 4-space

2009-05-24

arxiv.org/abs/0905.3872v3

Mathematics

Symplectic Geometry

18 pages. Typos corrected. The role of linking class was clarified following referee's suggestion

Scientific paper

We determine the Lagrangian monodromy group L(T) and the smooth monodromy group S(T) of a Clifford torus T in the symplectic 4-space. We show that L(T) is isomorphic to the infinite dihedral group, and S(T) is generated by three reflections. We give explicit formulas for both groups. We also show that if a Lagrangian torus is smoothly isotopic to a Clifford torus then the smooth isotopy can be chosen to be Lagrangian outside of a disc.

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