Canonical models of filtered $A_\infty$-algebras and Morse complexes

Simple item page
dc.creatorFukaya, K.
dc.creatorOH, Y. -G.
dc.creatorOhta, H.
dc.creatorOno, K.
dc.date2008-12-10
dc.date.accessioned2026-07-07T12:11:42Z
dc.date.available2026-07-07T12:11:42Z
dc.descriptionThe purpose of this paper is two-fold. First we explain the construction of the canonical model of filtered $A_\infty$-algebras given in the authors' book [FOOO]. The canonical model plays a crucial role in the study of Lagrangian Floer theory on toric manifolds in our recent papers, arXiv:0802.1703 and arXiv:0810.5654. Then using a variation of the arguments used in that construction, we define a natural filtered $A_\infty$-structure on the Morse complex of a Morse function and its $A_\infty$ homotopy to the $A_\infty$-algebras on a Lagrangian submanifold constructed in [FOOO]. The corresponding graphical moduli spaces `summing over trees' involve holomorphic discs connected by the gradient flow lines.
dc.description28 pages, 6 figures ; to appear in the proceedings of Eliashberg's 60th birthday conference (Yashafest)
dc.identifierhttps://arxiv.org/abs/0812.1963
dc.identifierhttp://arxiv.org/abs/0812.1963
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210303
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Geometry
dc.subject53D12, 53D40 ; 14J45, 14J32
dc.titleCanonical models of filtered $A_\infty$-algebras and Morse complexes
dc.typetext

Files

Collections

arXiv