Abstract
Since spectral invariants were introduced in cotangent bundles via generating functions by Viterbo in the seminal paper [73], they have been defined in various contexts, mainly via Floer homology theories, and then used in a great variety of applications. In this paper we extend their definition to monotone Lagrangians, which is so far the most general case for which a "classical" Floer theory has been developed. Then, we gather and prove the properties satisfied by these invariants, and which are crucial for their applications. Finally, as a demonstration, we apply these new invariants to symplectic rigidity of some specific monotone Lagrangians.
| Original language | English |
|---|---|
| Pages (from-to) | 627-700 |
| Number of pages | 74 |
| Journal | Journal of Topology and Analysis |
| Volume | 10 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Sep 2018 |
Bibliographical note
Publisher Copyright:© 2018 World Scientific Publishing Company.
Keywords
- Lagrangian Floer homology
- Symplectic manifolds
- monotone Lagrangian submanifolds
- quantum homology
- spectral invariants
ASJC Scopus subject areas
- Analysis
- Geometry and Topology