1.1 Background The subject of this book is Morse homology as a combination of relative
Morse theory and Conley's continuation principle. The latter will be useda s an instrument to
express the homology encoded in a Morse complex associated to a fixed Morse function …

This book is based on the lecture notes from a course we taught at Penn State University
during the fall of 2002. The main goal of the course was to give a complete and detailed
proof of the Morse Homology Theorem (Theo rem 7.4) at a level appropriate for second year …

Abstract. Given a smooth projective toric variety X, we construct an A∞ cat- egory of Lagrangians
with boundary on a level set of the Landau–Ginzburg mirror of X. We prove that this category
is quasi-equivalent to the DG cate- gory of line bundles on X … Mathematics Subject Classification …

An explicit isomorphism between Morse homology and singular homology is constructed via
the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a
Morse function, the unstable manifolds for the negative gradient flow are compactified in a …

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each
action window are compact up to breaking one gets a bidirect system of chain complexes.
There are different possibilities to take limits of such a bidirect system. We discuss in this …

We prove that there exists a canonical level-preserving isomorphism between the stable
Morse homology (or the Morse homology of generating functions) and the Floer homology
on the cotangent bundle $ T^* M $ for any closed submanifold $ N\subset M $ for any …

We propose a new topological method for shape description that is suitable for any multi-
dimensional data set that can be modelled as a manifold. The description is obtained for all
pairs (M, f), where M is a closed smooth manifold and fa Morse function defined on M. More …

The Fukaya category of a Weinstein manifold is an intricate symplectic invariant of high
interest in mirror symmetry and geometric representation theory. This paper informally
sketches how, in analogy with Morse homology, the Fukaya category might result from …

The purpose of the paper is to give an alternative construction and the proof of the main
properties of symplectic invariants developed by Viterbo. Our approach is based on Morse
homology theory. This is a step towards relating the``finite dimensional''symplectic invariants …

We use the heat flow on the loop space of a closed Riemannian manifold—viewed as a
parabolic boundary value problem for infinite cylinders—to construct an algebraic chain
complex. The chain groups are generated by perturbed closed geodesics. The boundary …