2009/05/24 by Mei-Lin Yau, Yau, Mei-Lin
Mathematics · #53D12 #57R52 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0905.3872
openalex publication_date 2009/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.