These pages are intended as a service to those mathematicians interested in Strong Shape and Proper Homotopy Theory. They will give a brief list of the membership and location of research groups in these areas within the general European area. The list will not pretend to be exhaustive, but anyone wanting a mention can contact me and I will add in a short mention of their research.
At present it is not envisaged that links with neighbouring areas will be covered although that is clearly desirable!
T.P., 25/10/05
The group is centered on these two universities. The Addresses are:
University of Zaragoza,
Researchers: S. Ardanza, J. Cabeza, M.C. Elvira, J.M. Garcìa
Calcines, L.J. Hernández.
Researchers: J.I. Extremiana, M.T. Rivas.
Topics of interest:
Proper homotopy:
Closed model categories for proper homotopy, simplicial M-sets and
proper homotopy, algebraic models for proper $n$-types, stable proper homotopy.
Shape theory:
Simplicial M-sets for shape theory, fundamental pro-groupoid and covering
spaces, pro-homotopy theory, Steenrod and Cech homology theories.
The research team consists of J.M.R. Sanjurjo, M.A. Morón and F.R. Ruiz del Portal together with research students. Their addresses are:
J.M.R. Sanjurjo and F.R. Ruiz del Portal
email: sanjurjo@sungt1.mat.ucm.es (for sanjurjo)
(There are several other mathematicians also at Madrid that have published papers in the strong shape and proper homotopy area.)
Topics of interest
Strong shape theory
Multivalued maps and strong shape morphisms, Cech and Steenrod spaces
of loops, Topologies on sets of shape morphisms.
Applied strong shape theory
Strong shape and dynamical systems, strong shape of asymptotically
stable global attractors, strong shape of uniform attractors.
The team, as such, consists of T. Porter and research students. The address is:
School of Mathematics
Topics of interest:
Proper homotopy
Algebraic models for proper homotopy types, proper analogues of fibre
bundles and stacks,
Strong shape theory
Abstract strong shape theory and homotopy coherence, equivariant strong
shape theory, links between strong shape and the non- commutative algebraic
homotopy of C*-algebras. 'Non-commutative' strong shape and homotopy of
quantales. Rational strong shape theory using DG-algebras, coherent nerves.
Applied strong shape theory
Rational strong shape, fractals and strange attractors; dualised strong
shape, controlled homotopy and coarse geometry.
This area is one of the several under study by H.J. Baues and research
students at the Max Planck Institute, Bonn.
Topics of interest
Proper homotopy theory
Foundations of proper homotopy theory, applications of algebraic proper
homotopy theory to 'low dimensional' topology.