Homotopy of functions on non-metrizable manifolds, by David Gauld

Topology Atlas Document # taic-02.htm | Production Editor: R. Flagg

Topology Atlas Invited Contributions, vol. 1, issue 5 (1996), 71.

Homotopy of functions on non-metrizable manifolds
by

David Gauld

(Dept of Mathematics, The University of Auckland)

As far as I know I started this particular aspect of non-metrisable manifolds. I feel that the study of non-metrisable manifolds is a really exciting field and enjoyed reading Peter Nyikos' papers on the topic. The near characterisation of omega-bounded surfaces led me to wonder what happens to homotopy and isotopy classes of homeomorphisms on such surfaces, knowing that this theory was well worked out for compact surfaces and recognising that omega-boundedness and compactness have some features in common. Unfortunately, as seen in my paper in the proceedings of the Mary-Ellen Rudin retirement conference ["Homeomorphisms of 1-manifolds and w-bounded 2-manifolds", Papers on General Topology and Applications, 704(1993), 142-149], I was unable to make much progress, a situation which persists.

Received by the editors: January 26, 1996.