David Gauld
Foliations on non-metrisable manifolds: absorption by a Cantor black hole.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: David Gauld, Mathieu Baillif, Alexandre Gabard
Subjects: General Topology
AbstractWe investigate contrasting behaviours emerging when studying foliations on
non-metrisable manifolds. It is shown that Kneser's pathology of a manifold
foliated by a single leaf cannot occur with foliations of dimension-one. On the
other hand, there are open surfaces admitting no foliations.Metrisability of Manifolds.
Wed, 10/07/2009 - 12:26 — SomNambulAuthors: David Gauld
Subjects: General Topology
AbstractManifolds have uses throughout and beyond Mathematics and it is not
surprising that topologists have expended a huge effort in trying to understand
them. In this article we are particularly interested in the question: `when is
a manifold metrisable?' We describe many conditions equivalent to
metrisability.Metrisability of Manifolds.
Wed, 10/07/2009 - 12:26 — SomNambulAuthors: David Gauld
Subjects: General Topology
AbstractManifolds have uses throughout and beyond Mathematics and it is not
surprising that topologists have expended a huge effort in trying to understand
them. In this article we are particularly interested in the question: `when is
a manifold metrisable?' We describe many conditions equivalent to
metrisability.Homeomorphisms of Bagpipes.
Wed, 10/07/2009 - 12:26 — SomNambulAuthors: David Gauld
Subjects: General Topology
AbstractWe investigate the mapping class group of an orientable $\omega$-bounded
surface. Such a surface splits, by Nyikos's Bagpipe Theorem, into a union of a
bag (a compact surface with boundary) and finitely many long pipes. The
subgroup consisting of classes of homeomorphisms fixing the boundary of the bag
is a normal subgroup and is a homomorphic image of the product of mapping class
groups of the bag and the pipes.
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