Topology Seminar

Mustafa Cengiz (Boston College)
Heegaard genus and the complexity of fibered knots

Translation distance is a measure of the complexity of a fibered knot/link. Saul Schleimer conjectured that for every 3-manifold, there is a number that bounds the translation distance of any fibered knot in that manifold. By studying the interaction between Heegaard splittings and fibered knots, we confirm Schleimer’s conjecture for fibered knots which do not induce minimal genus Heegaard splittings. More precisely, we show (1) any non-trivial fibered knot in the 3-sphere has translation distance less than or equal 3, and (2) if a 3-manifold has Heegaard genus $g$ greater than 0, then any fibered knot that has translation distance greater than $2g+2$ induces a minimal genus Heegaard splitting.

Event Date: 
October 31, 2019 - 2:00pm to 2:50pm
217 MLH
Calendar Category: 
Seminar Category: 
Geometry and Topology