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Adam Clay, RLM 12.166: Circular orderings, amalgamation and 3-manifolds
Monday, November 12, 2018, 02:00pm - 03:00pm
A conjecture of Boyer, Gordon, Watson (and later Juhasz) postulatesa connection between the Heegaard-Floer homology of a 3-manifold,whether or not the 3-manifold supports a taut foliation, andleft-orderability of its fundamental group. In practice, however,it is turning out that most affirmative left-orderability resultsseem to arise from first considering circular orderability ofthe fundamental group, and then making an Euler class argumentto arrive at left-orderability via the construction of a lift.In this talk I will therefore introduce circular orderings ofgroups, and precisely explain the "lifting" notion of the previousparagraph and the cohomological obstructions to obtaining a left-orderingfrom a circular ordering. I'll also explain how a recent resultwith Ty Ghaswala concerning circular orderings of free productswith amalgamation will hopefully open the door to creating circularand left-orderings of fundamental groups of non-geometric 3-manifolds.
Location: RLM 12.166

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