Hamiltonian non-isotopy between the Clifford torus and the Chekanov torus in $\R^4$

The topic of this expository master's thesis concerns proving the Hamiltonian non-isotopy between the monotone Clifford torus and the Chekanov torus in \R⁴ 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].

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Si, Aerim

Contributors dc:contributor

• Kerman, Ely

• Hamiltonian isotopy invariant
• Clifford torus
• Chekanov torus.

Statement dc:rights

• Copyright 2021 Aerim Si

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/110739

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/110739