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Toroidal 3-manifolds and properties NLS, LO and CTF


Speaker: Cameron Gordon, U. Texas Austin
Location: Zoom
Start time: Tue, Feb 23 2021, 1:10PM

The L-space Conjecture says that for a prime 3-manifold, properties NLS (not being an L-space), LO (having left-orderable fundamental group), and CTF (supporting a co-orientable taut foliation), are equivalent. We investigate these properties for toroidal 3-manifolds. In particular we show that the cyclic branched covers of a prime satellite knot are NLS and LO, and are CTF if its companion is fibered. A partial extension to links shows that a prime quasi-alternating link is either hyperbolic or a (2,q) torus link. This is joint work with Steve Boyer and Ying Hu.