Morse Homology on Noncompact Manifolds

Abstract

Abstract. 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 note the relation between these different limits.

Rabinowitz–Floer Homology on Brieskorn Spheres: Fig. 1.

“…In this section, we present an axiomatic model for Morse and Floer theory over possibly non-compact manifolds. We follow [15], who claim that it all goes back to a suggestion made by D. Salamon. The Main Theorem 81 states that the two basic approaches in this setup -working over a Novikov completion or taking limits -yields the same homology, i.e.…”

“…that F H ∼ = lim b] . Our proof of this crucial theorem is less abstract (compared to [15], though perhaps tedious) and completely selfcontained.…”

Symplectic Tate homology

“…In this section we collect some algebraic facts, most of which can be found in [14]. For the applications we have in mind we have to work in the category of graded Z-modules.…”

The Rabinowitz–Floer homology for a class of semilinear problems and applications

“…for h ≥ c > 0. Then using the Rabinowitz-Floer homology, as in [16], we have that problem (9) has an infinite sequence of solution, with energy going to infinity. Indeed this problem falls into the class of operators for which we can use the methods we introduced in this paper.…”