\n Suppose that \\(M\\) is a closed\, connected\,\n or iented three-manifold which is not graph. All previously\n known c onstructions of taut foliations on such \\(M\\) used\n branched sur faces. These branched surfaces come from sutured\n manifold hierar chies\, following Gabai\, come from spanning\n surfaces of knot ext eriors\, following Roberts\, or come from\n one-vertex triangulatio ns with foliar orientations\, following\n Dunfield.\n
\n\n In this talk\, we give a new construction that does not u se\n branched surfaces. Instead\, we build a taut foliation from\n the data of a Heegaard diagram for \\(M\\) and a left order on\n the fundamental group \\(\\pi_1(M)\\). We glue an\n \\(\\mat hbb{R}\\)-transverse foliation (over a thickened Heegaard\n surface ) to a pair of handlebody foliations\; we then suitably\n cancel an y singularities. For Heegaard diagrams satisfying\n mild condition s\, this can be done reliably in Heegaard genus\n two. In some cas es this construction can be extended to\n higher Heegaard genus. T his helps explain numerical results\n of Dunfield: (i) tens of thou sands of Heegaard-genus two\n hyperbolic L-spaces certifiably fail to admit fundamental\n group left orders and (ii) no hyperbolic L-s pace is known to\n admit a fundamental group left order.\n
\n LOCATION:https://researchseminars.org/talk/GaTO/23/ END:VEVENT END:VCALENDAR