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 independent of this function. Originally, this type of
Morse-theoretical tool was developed by Andreas Floer in order to
find a proof of the famous Arnold conjecture, whereas classical
Morse theory turned out to fail in the infinite-dimensional
setting. In this framework, the homological variant of Morse theory
is also known as Floer homology. This kind of homology theory is
the central topic of this book. But first, it seems worthwhile to
outline the standard Morse theory. 1.1.1 Classical Morse Theory The
fact that Morse theory can be formulated in a homological way is by
no means a new idea. The reader is referred to the excellent survey
paper by Raoul Bott [Bol.
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