Presentation of Degree Project E

  • Date: –10:00
  • Lecturer: Zixuan Wang
  • Contact person: Georgios Dimitroglou Rizell
  • Seminarium

Local unknottedness of planar Lagrangians with boundary

The presentation will take place on Zoom.

Abstract: We show the smooth version of the nearby Lagrangian conjecture for the 2-dimensional pair of pants and the Hamiltonian version for the cylinder. In other words, for any closed exact Lagrangian submanifold of $T^{*}M$, there is a smooth or Hamiltonian isotopy, when M is a pair of pants or a cylinder respectively, from it to the zero section. For the pair of pants, we study some results from pseudo-holomorphic curve theory, then use Moser's linear construction and compactification to construct a smooth isotopy. For the cylinder, we modify a result of G. Dimitroglou Rizell for certain Lagrangian tori to show that it actually gives the Hamiltonian isotopy for a Lagrangian cylinder.