This self-contained treatment of Morse theory focuses on applications and is intended for a
graduate course on differential or algebraic topology. The book is divided into three …

This paper is a progress report on our efforts to understand the homotopy theory underlying
Floer homology. Its objectives are as follows:(A) to describe some of our ideas concerning …

Critical points of functions and gradient lines between them form a cornerstone of physical
thinking. In Morse theory the topology of a manifold is investigated in terms of these notions …

Let X be a closed oriented Riemannian manifold with χ (X)= 0 and b1 (X)> 0, and let φ: X→ S
1 be a circle-valued Morse function. Under some mild assumptions on φ, we prove a formula …

Abstract We construct a Hamiltonian Floer theory-based invariant called relative symplectic
cohomology, which assigns a module over the Novikov ring to compact subsets of closed …

In principle, Floer theory can be extended to define homotopy invariants of families of
equivalent objects (eg Hamiltonian isotopic symplectomorphisms, 3–manifolds, Legendrian …

We begin with a summary of Morse theory in order to fix notation. For more background see
eg Austin and Braam [2], Bott [3], Hutchings [9], Milnor [12], Morse [13], Schwarz [19], Weber …

In this paper we present a new approach to Morse theory based on the de Rham-Federer
theory of currents. The full classical theory is derived in a transparent way. The methods …

SOON after Donaldson introduced his polynomial invariants for 4-manifolds, the obvious
question-how to compute these invariants through cut and paste operations-became a …

This is mainly a survey of recent work on algebraic ways to “measure „moduli spaces of
connecting trajectories in Morse and Floer theories as well as related applications to …