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Spectral invariants for monotone Lagrangians

Rémi Leclercq

Université Paris-Sud, Département de Mathématiques, Bat. 425, 91400 Orsay, France

E-mail Address: remi.leclercq@math.u-psud.fr

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and

Frol Zapolsky

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

E-mail Address: frol.zapolsky@gmail.com

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https://doi.org/10.1142/S1793525318500267Cited by:24 (Source: Crossref)

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.

Keywords:

AMSC: Primary 57R17, Secondary 53D12, Secondary 53D40

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