Programme leader: J. van Mill
Description of the
The programme focuses on the study of the topology of
classical objects, like the Hilbert cube, continua in the plane which arise
in topological dynamics, various topological groups and the
Cech-Stone compactifications of the reals and the integers, as well as more
recent objects like certain compact L-spaces, spaces of chaotic maps and "nice"
two-point sets in the plane. Most of these objects are studied using methods from
several branches of general and geometric topology, as well as non-topological
methods, most notably from functional analysis, measure theory, set theory and
geometry. The topological methods can be as diverse as infinite-dimensional
topology, descriptive set theory, continuum theory and the theory of
ultrafilters. A good illustration of the kind of interaction one gets is provided
by the study of so-called colourings of maps, related to the question whether a
fixed-point-free selfmap f on X extends to a fixed-point-free
selfmap on the Cech-Stone compactification of X.
Here one meets
classical results from algebraic and geometric topology, like the
Ljusternik-Schnirelman theorem and the Borsuk-Ulam theorem, non-trivial results
in topological groups, methods from dimension theory and topological dynamics, as
well as set-theoretic methods to construct counterexamples.
This theory also
gives rise to applications in the form of fixed point theorems, for instance.
Of course similar things can be said for other specific research interests
within this programme.