Characterizing Slopes for Alternating Knots

Characterizing Slopes for Alternating Knots

Explore a 56-minute conference talk from the Gauge Theory and Low Dimensional Topology event, focusing on characterizing slopes for alternating knots. Delve into the concept of characterizing slopes for knots in the 3-sphere, examining the conjecture that all but finitely many non-integer slopes should be characterizing for a given knot. Learn about recent progress in this field, including methods to prove the conjecture for various knot classes, with particular emphasis on alternating knots. Gain insights into the oriented homeomorphism type of p/q-surgery on knots and its role in determining knot uniqueness among all knots in the 3-sphere.