Veering Dehn Surgery

Saul Schleimer (Warwick)

Monday 21st March, 2016 16:00-17:00 Maths 522



(Joint with Henry Segerman.) It is a theorem of Moise that
every three-manifold admits a triangulation, and thus infinitely many.
Thus, it can be difficult to learn anything really interesting about
the three-manifold from any given triangulation. Thurston introduced
''ideal triangulations'' for studying manifolds with torus boundary;
Lackenby introduced ''taut ideal triangulations'' for studying the
Thurston norm ball; Agol introduced ''veering triangulations'' for
studying punctured surface bundles over the circle. Veering
triangulations are very rigid; one current conjecture is that any
fixed three-manifold admits only finitely many veering triangulations.

After giving an overview of these ideas, we will introduce ''veering
Dehn surgery''. We use this to give the first infinite families of veering triangulations with various interesting properties.

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