Hamiltonian non-isotopy between the Clifford torus and the Chekanov torus in $\R^4$
Si, Aerim
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https://hdl.handle.net/2142/110739
Description
Title
Hamiltonian non-isotopy between the Clifford torus and the Chekanov torus in $\R^4$
Author(s)
Si, Aerim
Issue Date
2021-04-29
Director of Research (if dissertation) or Advisor (if thesis)
Kerman, Ely
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Hamiltonian isotopy invariant
Clifford torus
Chekanov torus.
Abstract
The topic of this expository master's thesis concerns proving the Hamiltonian non-isotopy between the monotone Clifford torus and the Chekanov torus in $\R^4$ by employing three Hamiltonian isotopy invariants: counting of Maslov index 2 pseudo-holomorphic discs with boundaries lying on the torus [EP], the Hamiltonian invariant associated to versal deformations and symplectic capacity [Ch1], and the Hamiltonian invariant defined by Hamiltonian monodromy group of the torus [Yau].
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