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Floer homology, group orders, and taut foliations of hyperbolic 3-manifolds

Presented by: 
Nathan Dunfield University of Illinois at Urbana-Champaign
Date: 
Monday 30th January 2017 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
Abstract: 
A bold conjecture of Boyer-Gorden-Watson and others posit that for any irreducible rational homology 3-sphere M the following three conditions are equivalent: (1) the fundamental group of M is left-orderable, (2) M has non-minimal Heegaard Floer homology, and (3) M admits a co-orientable taut foliation. Very recently, this conjecture was established for all graph manifolds by the combined work of Boyer-Clay and Hanselman-Rasmussen-Rasmussen-Watson. I will discuss a computational survey of these properties involving half a million hyperbolic 3-manifolds, including new or at least improved techniques for computing each of these properties. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons