Geometry and Topology Seminar: "Slope detection and cyclic branched covers of satellite knots"

Abstract: 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 (admitting a co-orientable taut foliation), are equivalent. We investigate these properties for toroidal 3-manifolds through the notion of slope detection. 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. This is joint work with Steve Boyer and Cameron Gordon.

Host: Steven Frankel