Günter Rote:
Piecewise linear Morse theory
In: Oberwolfach Reports, 3, European Mathematical Society -
Publishing House, 2006, pp. 696–698. doi:0.4171/OWR/2006/12
Abstract
Classical Morse Theory considers the topological changes of the level
sets
Mh={x in M | f(x)=h}
of a smooth function f defined on a
manifold M as the height h varies. At critical
points, where
the gradient of f vanishes, the topology changes. These changes
can be
classified locally, and they can be related to global topological
properties
of M. Between critical values, the level sets vary smoothly. We
prove
that the same statement is true for piecewise linear
functions in up
to three variables: between critical values, all level sets are
isotopic.
Last update: June 12, 2007.