Spectral invariants for monotone Lagrangians

By R. Leclercq, F. Zapolsky. Journal of Topology and Analysis (JTA), 2015

56 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b4636cae8ec08d9821dbda8931a5a297daab59b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Persistence modules with operators in Morse and Floer theory (2017, background): “Spectral invariant can be defined in complete generality (without assumptions on π2(M)), and have been used extensively in symplectic topology in the last few decades starting with the foundational papers [42,51,57] (see [40,53] for recent developments and numerous further references), before persis”
Bounds on spectral norms and barcodes (2018, methodology): “t to note that the two spectral norms (H); (L;H) for H2H featured above are related as follows. Lemma 4. Let Lin Mbe monotone, with N L2:Then for each H2H; (L;H) (H): Proof. Using Proposition 4 in [65], we have the following relation between the relative and absolute spectral invariants. c(L;[M] [L”