U.W. Bangor - School of Informatics
Mathematics Preprints 2001
Semigroup and Automata Theory
01.13 : LAWSON, M.V. & MATTHEWS, J.
The universal group of an inverse semigroup
Abstract:We define the universal group of an inverse semigroup with zero and examine its properties.
In the case of inverse semigroups without zero we recapture the familiar minimum group congruence.
- to be replaced by an up-dated version.
01.14 : LAWSON, M.V., MATTHEWS, J. & PORTER, T.
The homotopy theory of inverse semigroups
Abstract:We show that abstract homotopy theory can be used to define a suitable notion of homotopy equivalence for inverse semigroups.
As an application of our theory, we prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function can be factorised into a homotopy equivalence followed by a fibration.
We show that this factorisation is isomorphic to the one constructed by Steinberg in his `Fibration Theorem', originally proved using a generalisation of Tilson's derived category.