Lagrangian Cobordisms in Liouville manifolds

Abstract

Floer theory for Lagrangian cobordisms was developed by Biran and Cornea to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.

43 pages, 12 figures, new subsections 5.3, 5.4

References in corpus (5)

• Higher Segal structures in algebraic $K$-theory
• The symplectic geometry of higher Auslander algebras: Symmetric products of disks
• The Fukaya category pairs with Lagrangian cobordisms
• Cyclic structures and broken cycles
• Lagrangian cobordism groups of higher genus surfaces

Cited by in corpus (2)

• Aspects of functoriality in homological mirror symmetry for toric varieties
• Algebraic Lagrangian cobordisms, flux and the Lagrangian Ceresa cycle