Homological algebra related to surfaces with boundary

Abstract

In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL${}_{\infty }$-algebras.

127 pages, 22 figures. Some references added in version 2. Fixed a tex problem in version 3

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• The $L_{\infty }$-structure on symplectic cohomology
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