Heegaard Foliations: Taut foliations from Left Orders in Heegaard genus 2
Abstract: One of the driving questions of low dimensional topology is how a manifold's fundamental group relates to fundamental features of, or structures on, that manifold. As one example of this, for decades dating back at least to work of Thurston, there has been an open question of whether it is possible to derive a taut foliation on an irreducible 3-manifold from a fundamental group real line action, in any but the most tautological of cases. In this talk, I describe a novel construction in which I produce a taut foliation from a fundamental group real line action (if such action exists) for any Heegaard-genus-2 irreducible 3-manifold, under mild conditions. The construction extends to higher Heegaard genus in special cases. This also provides one of the first, if not only, examples of a taut foliation construction on a non-fibered hyperbolic 3-manifold without recourse to branched surfaces.
Dr. Rasmussen received her PhD from Harvard University in 2009 and is currently an EPSRC Research Fellow at the University of Cambridge.
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