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SUMMARY:Connecting essential triangulations [MPIM]
DTSTART:20250408T090000Z
DTEND:20250408T100000Z
DTSTAMP:20260913T021400Z
UID:indico-event-309@math-events.uni-bonn.de
DESCRIPTION:Speakers: Kalelkar Tejas (Indian Institute of Science Educatio
 n and Research/MPIM)\n\nLow-dimensional topology seminar. \nLet M be a 3-
 dimensional compact manifold with non-empty boundary. There exists a colle
 ction of tetrahedra stuck in pairs along their faces such that deleting al
 l their vertices gives a space that is homeomorphic to the interior of M. 
 This is called a (ideal) triangulation of M. Amendola\, Matveev and Pierga
 llini have shown that any two such triangulations of M are connected by a 
 sequence of triangulations\, where each triangulation in the sequence is o
 btained from the previous one by a local combinatorial change\, namely a 2
 -3 or 3-2 move. For some applications however\, we need our triangulations
  to have special properties. We call a triangulation essential if none of 
 its edge is a homotopically trivial loop. Certain essential triangulations
  are isolated\, in the sense that any 2-3 or 3-2 move introduces an inesse
 ntial edge. We have shown that when the universal cover of M has infinitel
 y many boundary components and the two given essential triangulations of M
  are not isolated\, then they are connected by a sequence of 2-3 and 3-2 m
 oves through essential triangulations. If in addition\, we allow V-moves a
 nd their inverses\, then any two essential triangulations (including the i
 solated ones) are connected via essential triangulations. Our results have
  applications such as proving that the 1-loop invariant is independent of 
 the choice of triangulation. This is joint work with Saul Schleimer and He
 nry Segerman. \n\nhttps://math-events.uni-bonn.de/event/309/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/309/
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