Morse sequences
Gilles Bertrand
We introduce the notion of a Morse sequence, which provides a simple and
effective approach to discrete Morse theory. A Morse sequence is a sequence
composed solely of two elementary operations, that is, expansions (the inverse
of a collapse), and fillings (the inverse of a perforation). We show that a
Morse sequence may be seen as an alternative way to represent the gradient
vector field of an arbitrary discrete Morse function. We also show that it is
possible, in a straightforward manner, to make a link between Morse sequences
and different kinds of Morse functions. At last, we introduce maximal Morse
sequences, which formalize two basic schemes for building a Morse sequence from
an arbitrary simplicial complex.