The use of Web Ontology Language (OWL) to Combine Extant Controlled Vocabularies in Biodiversity Informatics Appears Redundant

Implementation of PESI requires data to be combined from multiple source databases. Some of the shared fields in the source databases used different controlled vocabularies of terms. OWL DL was investigated as a mechanism to build an extensible, shared ontology of species occurrence terms that permitted the source database to continue using and extending their own vocabularies whilst formally mapping to a more generic shared vocabulary. The merits of this approach were explored and it was concluded that the building of such a complex mapping ontology probably wasn't worthwhile. The level of semantic complexity involved outweighed the costs of simply imposing a flat list of well defined terms onto data suppliers. The main problem with exiting vocabularies appear to be the overloading of terms. A candidate list of terms was proposed

Period three actions on the three-sphere

We show that a free period three action on the three-sphere is standard, i.e. the quotient is homeomorphic to a lens space. We use a minimax argument involving sweepouts.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper11.abs.htm

Genus two Heegaard splittings of orientable three-manifolds

It was shown by Bonahon-Otal and Hodgson-Rubinstein that any two genus-one Heegaard splittings of the same 3-manifold (typically a lens space) are isotopic. On the other hand, it was shown by Boileau, Collins and Zieschang that certain Seifert manifolds have distinct genus-two Heegaard splittings. In an earlier paper, we presented a technique for comparing Heegaard splittings of the same manifold and, using this technique, derived the uniqueness theorem for lens space splittings as a simple corollary. Here we use a similar technique to examine, in general, ways in which two non-isotopic genus-two Heegard splittings of the same 3-manifold compare, with a particular focus on how the corresponding hyperelliptic involutions are related.Comment: 65 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper24.abs.htm

Inflations of ideal triangulations

Starting with an ideal triangulation of the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulations of M itself. Besides a step-by-step algorithm for such a construction, we provide examples of an inflation of the two-tetrahedra ideal triangulation of the complement of the figure-eight knot in the 3-sphere, giving a minimal triangulation, having ten tetrahedra, of the figure-eight knot exterior. As another example, we provide an inflation of the one-tetrahedron Gieseking manifold giving a minimal triangulation, having seven tetrahedra, of a nonorientable compact 3-manifold with Klein bottle boundary. Several applications of inflations are discussed.Comment: 48 pages, 45 figure