SMS scnews item created by Catherine Meister at Fri 6 Mar 2026 1107
Type: Seminar
Distribution: World
Expiry: 20 Mar 2026
Calendar1: 11 Mar 2026 1200-1300
CalLoc1: SMRI Seminar Room (A12 Macleay Room 301)
CalTitle1: Non-additivity of the unknotting number
Auth: cmeister@159-196-153-133.9fc499.syd.nbn.aussiebb.net (cmei0631) in SMS-SAML
Geometry & Topology Seminar: Boden
Non-additivity of the unknotting number
Hans Boden, McMaster University
Geometry & Topology Seminar, Wednesday 11th March 2026, 12 pm – 1 pm, SMRI Seminar Room (A12 Macleay Room 301)
Abstract: Every knot diagram can be converted into an unknot diagram by applying crossing changes. For a given knot, the minimum number of crossing changes needed, taken over all representative diagrams, is the unknotting number of that knot. In 1937 Wendt studied the unknotting number of composite knots, namely those of the form K # J. He posited that the unknotting number of K # J should be equal to the sum of the unknotting numbers of K and and that of J. Early evidence in support of the conjecture came from Marty Scharlemann, who in 1985 proved it for knots K, J with unknotting number one. The goal of the talk is to survey two recent preprints disproving the conjecture. The preprints are due to Mark Brittenham and Susan Hermiller, and their discovery has been a major breakthrough and suggests that knot theorists really do not understand unknotting at all well!
The Geometry & Topology Seminar will be held on the second and fourth Wedensday of the month during semester. The Australian Geometric Topology Webinar will be broadcast at the same time and place on the first and third Wednesday of the month. For seminar updates, see Geometry & Topology Seminar.