A new higher homotopy groupoid:
the fundamental globular omega-groupoid of a filtered space
Summary:
We use the n-globe with its skeletal filtration to define
the fundamental globular omega-groupoid of a filtered space;
the proofs use an analogous fundamental cubical omega--groupoid
due to the author and Philip Higgins.
This method also relates the construction to the fundamental crossed complex
of a filtered space, and this relation allows the proof that
the crossed complex associated to the free globular omega-groupoid
on one element of dimension n is the fundamental crossed complex
of the n-globe.
Possible connections between whiskered categories and groupoids,
many object Lie algebras, automorphism structures
and local-to-global questions
Summary:
We define the notion of whiskered categories and groupoids
and discuss potential applications, relations betweens topics,
extensions, for example to a many object Lie theory,
to automorphism structures for crossed modules,
and to resolutions of monoids.
This paper is more an outline of a possible programme or programmes
and their relationships than giving conclusive results.
