ar X iv : 0 90 3 . 01 12 v 1 [ m at h . G T ] 2 8 Fe b 20 09 Coverings and Minimal Triangulations of 3 – Manifolds

ar X iv : 0 90 6 . 48 64 v 1 [ m at h . G T ] 2 6 Ju n 20 09 ZZ 2 – Thurston Norm and Complexity of 3 – Manifolds

A new lower bound on the complexity of a 3–manifold is given using the ZZ2 –Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characterised using normal surfaces consisting entirely of quadrilateral discs. AMS Classification 57M25, 57N10

ar X iv : 0 90 2 . 29 25 v 1 [ m at h . G T ] 1 7 Fe b 20 09 COVERINGS AND ACTIONS OF STRUCTURED LIE GROUPOIDS

In this work we deal with coverings and actions of Lie groupgroupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-groupoids on Lie groups and the category of smooth coverings of Lie group-groupoids.

ar X iv : m at h / 04 02 39 3 v 1 [ m at h . G T ] 2 4 Fe b 20 04 CYCLIC BRANCHED COVERINGS OF ( g , 1 ) - KNOTS

We study (g, 1)-knots and their strongly-cyclic branched coverings, proving the necessary and sufficient conditions for their existence and uniqueness, and characterizing their fundamental groups. As a relevant example, we prove that generalized periodic Takahashi manifolds belong to this family of manifolds.

ar X iv : 0 90 2 . 39 12 v 1 [ m at h . G R ] 2 3 Fe b 20 09 Brent Everitt The Combinatorial Topology

ar X iv : 0 90 2 . 32 39 v 1 [ m at h . D G ] 1 8 Fe b 20 09 Gauge theory in higher dimensions , II