The Viterbo-Maslov Index in Dimension Two
Joel Robbin, Dietmar Salamon
TL;DR
This paper establishes a formula linking the Viterbo-Maslov index of a smooth strip in a 2-manifold to a degree function, enhancing understanding of symplectic invariants in low-dimensional topology.
Contribution
It provides a new explicit formula for the Viterbo-Maslov index in dimension two, relating it to the degree function on the complement of boundary submanifolds.
Findings
Derived a formula for the Viterbo-Maslov index in 2D
Connected symplectic invariants with topological degree theory
Enhanced computational tools for symplectic topology in low dimensions
Abstract
We prove a formula that expresses the Viterbo-Maslov index of a smooth strip in an oriented 2-manifold with boundary curves contained in 1-dimensional submanifolds in terms the degree function on the complement of the union of the two submanifolds.
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
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals