Morse homology: orientation of the moduli space of gradient flow lines, coherence and applications

Abstract

In this paper, we shall compute the chain complex and the corresponding homology of some Morse function $f$ over integer coefficients. The definition of the correct boundary operator requires a careful construction of moduli space of (pseudo)gradient flow lines orientations. We will then apply this construction in the computation of these homology groups on 4-manifolds.

22 pages, in French, v4 clarifications and references added

References in corpus (2)

• Existence and multiplicity of solutions for double-phase Robin problems
• The moduli space of gradient flow lines and Morse homology