Reeb dynamics in dimension 3 and broken book decompositions

Reeb dynamics in dimension 3 and broken book decompositions

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Vincent Colin, Université de Nante

Zoom link:  :  https://umontreal.zoom.us/j/94366166514?pwd=OHBWcGluUmJwMFJyd2IwS1ROZ0FJdz09    

Backup/Alternate:  https://theias.zoom.us/j/98165917888?pwd=bitwUVFVdjdVb1F3OTZTQTNqWHJjUT09

 

In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate Reeb vector field has either 2 or infinitely periodic orbits and that on a closed 3-manifold that is not graphed, every nondegenerate Reeb vector field has positive topological entropy.