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Topology/Geometry Seminar

Slope detection and toroidal 3-manifolds

Ying Hu (University of Nebraska Omaha)

Location:  zoom link: https://rutgers.zoom.us/j/98782700784?pwd=UFhEdTc4NlF6QlljZXlweElCSUVDdz09
Date & time: Tuesday, 01 March 2022 at 3:50PM - 4:50PM

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. We show that all toroidal integer homology spheres are LO, and that the n-fold cyclic branched covers of a prime satellite knot are NLS and LO, and are CTF if its companion is fibered. We also prove a partial extension of the latter result to links and confirm a folklore conjecture that prime satellite links are never quasi-alternating. 

This is joint work with Steve Boyer and Cameron Gordon.

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