This is a two-volume series research monograph on the general Lagrangian Floer theory
and on the accompanying homological algebra of filtered $ A_\infty $-algebras. This book …

Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture,
covering some varieties of general type. We prove a version of this conjecture in the simplest …

We prove that the wrapped Fukaya category of any $2 n $-dimensional Weinstein manifold
(or, more generally, Weinstein sector) $ W $ is generated by the unstable manifolds of the …

In this article we use a continuous family of multisections of the moduli space of
pseudoholomorphic discs to partially improve the construction of the Lagrangian Floer …

The main purpose of this book is to present a complete self-contained explanation of the
virtual fundamental chain technique via the Kuranishi structure introduced by Fukaya–Ono …

Let. M; J; g;/be a Calabi–Yau m-fold, and consider compact, graded Lagrangians L in M.
Thomas and Yau [81, 82] conjectured that there should be a notion of 'stability'for such L …

A bstract Recently we discussed new aspects of degenerate brane configurations, which
can appear in the context of heterotic strings, perturbative type II, or M/F-theory. Here we …

Ideas of Fukaya and Kontsevich-Soibelman suggest that one can use Strominger-Yau-
Zaslow's geometric approach to mirror symmetry as a torus duality to construct the mirror of a …

To a nullhomologous knot $ K $ in a 3-manifold $ Y $, knot Floer homology associates a
bigraded chain complex over $\mathbb {F}[U, V] $ as well as a collection of flip maps; we …

The $ n $-dimensional pair of pants is defined to be the complement of $ n+ 2$ generic
hyperplanes in $\mathbb {CP} n $. We construct an immersed Lagrangian sphere in the pair …