Topology Seminar (Introductory Talk): Symmetric unions without crossing changes

Seminar | April 26 | 2:10-3 p.m. | 736 Evans Hall

 Allison Moore, UC Davis

 Department of Mathematics

A classic problem in knot theory is the cosmetic crossing conjecture. This conjecture asserts that a crossing change will always change the knot type, unless the crossing is nugatory. In the main seminar I'll describe an obstruction to so-called "cosmetic" crossing changes. In the student seminar, I'll show how to use that obstruction to produce new infinite families of knots for which the conjecture is true. In the process, we'll review branched double covers, L-spaces, and discuss a computational technique which arises in various homology theories.