Homological Lagrangian monodromy and Wang exact sequence
Yoshihiro Sugimoto
TL;DR
This paper investigates the homological monodromy of Lagrangian submanifolds, establishing conditions under which it is trivial based on energy constraints related to Hamiltonian isotopies and J-holomorphic spheres and discs.
Contribution
It provides a new criterion for triviality of homological Lagrangian monodromy using energy bounds involving J-holomorphic curves.
Findings
Homological Lagrangian monodromy is trivial under certain energy conditions.
Energy bounds related to J-holomorphic spheres and discs determine monodromy behavior.
The paper connects symplectic energy concepts with topological properties of Lagrangian submanifolds.
Abstract
In this paper, we study homological monodromy of a Lagrangian submanifold. We prove that homological Lagrangian monodromy is trivial if Hofer energy of a Hamiltonian isotopy is smaller than the minimum energy of J-holomorphic spheres and discs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology