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Asphericity Results for Labeled Oriented Tree Complexes

by Dr. Anthony Bedenikovic of Bradley U

  • Geometry/ Topology Seminar
  • Topology Seminar
When Tue, Oct 13, 2015
from 02:10 PM to 03:00 PM
Where 225 Ritter Hall
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Labeled oriented tree (LOT) complexes are 2-dimensional complexes whose structure is encoded in directed trees with vertex labels on their edges.  These complexes, it turns out, strongly resemble spines for classical knot complements in the 3-sphere.  In fact, every classical knot complement may be regarded as an LOT complex.

In light of this connection, it is natural to ask whether or not LOT complexes are aspherical, that is, whether or not their higher homotopy groups vanish.  In this talk we will explore the connection with classical knot complements and consider partial results relating to asphericity.  Beyond their role in 3-dimensional matters, LOT complexes are known to correspond to the complements of certain kinds of disks in the 4-ball.  We will use this higher-dimensional connection to obtain additional asphericity results.  The techniques here are visual for just a moment, then combinatorial.

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