Since spectral invariants were introduced in cotangent bundles via generating functions by Viterbo in the seminal paper , 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.
|Number of pages||74|
|Journal||Journal of Topology and Analysis|
|State||Published - 1 Sep 2018|
Bibliographical notePublisher Copyright:
© 2018 World Scientific Publishing Company.
- Lagrangian Floer homology
- Symplectic manifolds
- monotone Lagrangian submanifolds
- quantum homology
- spectral invariants
ASJC Scopus subject areas
- Geometry and Topology