On equivalence of two constructions of invariants of Lagrangian submanifolds.
type: Item
instance of: scholarly article
title: On equivalence of two constructions of invariants of Lagrangian submanifolds.
zbMATH Open document ID: 1033.53066
author: Darko Milinković
published in: Pacific Journal of Mathematics
publication date: 2000-12-03T00:00:00Z
review text: Recently \textit{Y.-G. Oh} [ J. Differ. Geom. 46, 499--577 (1997; Zbl 0926.53031)], defined symplectic invariants for certain Lagrangian submanifolds in the cotangent bundle \(T^*M\) (with its natural symplectic structure) of a compact manifold \(M\). His construction can be considered as an infinite dimensional version of the construction given earlier by \textit{C. Viterbo} [ Math. Ann. 292, 685--710 (1992; Zbl 0735.58019)]. In a previous paper, the author and Y.-G. Oh showed the relation between the above two invariants, constructing the invariants which interpolate the above two. In this paper, the author proves the details of the construction of the interpolated Floer-Morse theory on \(T^*(M \times {\mathbb R}^m)\) with an arbitary coefficient ring. Moreover, an application of his result to Hofer's geometry of Lagrangian submanifolds is given.
reviewed by: Marisa Fernández
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 57R17
Mathematics Subject Classification ID: 53D40
zbMATH DE Number: 1537863
zbMATH Keywords: symplectic invariants
zbMATH Keywords: Lagrangian submanifolds
zbMATH Keywords: Floer-Morse theory
MaRDI profile type: Publication
OpenAlex ID: W2328729079
DOI: 10.2140/PJM.2000.195.371
description: scientific article; zbMATH DE number 1537863