College of Liberal Arts & Sciences

# Topology Seminar

Speaker:

Mustafa Cengiz (Boston College)

Topic:

Heegaard genus and the complexity of fibered knots

**Abstract: **

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 Schleimerâ€™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

Location:

217 MLH

Calendar Category:

Seminar

Seminar Category:

Geometry and Topology