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SUMMARY:From veering triangulations to dynamic pairs - Saul Schleimer (War
 wick)
DTSTART:20230208T160000Z
DTEND:20230208T170000Z
UID:TALK193981@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:Ideal triangulations were introduced by Thurston as a tool for
  studying hyperbolic three-manifolds.  Taut ideal triangulations were intr
 oduced by Lackenby as a tool for studying ``optimal'' representatives of s
 econd homology classes.\n\nAfter these applications in geometry and topolo
 gy\, it is time for dynamics.  Veering triangulations (taut ideal triangul
 ations with certain decorations) were introduced by Agol to study the mapp
 ing tori of pseudo-Anosov homeomorphisms.  Gueritaud gave an alternative c
 onstruction\, and then Agol and Gueritaud generalised it to give veering t
 riangulations for three-manifolds admitting pseudo-Anosov flows (without p
 erfect fits).\n\nWe prove the converse of their result: that is\, from any
  veering triangulation we produce a canonical dynamic pair of branched sur
 faces (in the sense of Mosher).  These give flows on appropriate Dehn fill
 ings of the original manifold.  Furthermore\, our construction and that of
  Agol--Gueritaud are inverses.  This then gives a ``perfect'' combinatoria
 lisation of pseudo-Anosov flow (without perfect fits).\n\nThis is joint wo
 rk with Henry Segerman.\n
LOCATION:MR13
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