
Department of Mathematics Calendar
Allison Miller, UT Austin, Winding number of satellite operators and concordance
- This event has passed.
Event Navigation
Historically, the study of the collection of concordance classes of knots has focused on understanding its group structure while devoting relatively little attention to the natural metric induced by the 4-genus. Cochran and Harvey investigated the metric properties of the maps on concordance induced by satellite operators, asking when two patterns P and Q are of bounded distance in their action on concordance. In this talk, I will describe the proof that two patterns are of bounded distance if and only if they have the same algebraic winding number [Cochran-Harvey, M.]. I’ll focus on the subtlest case, when P has winding number m and Q has winding number -m, and use Casson-Gordon signatures to show that for m>0 the 4-genus of P(K)#-Q(K) can be arbitrarily large.
Details
- Date
-
February 21, 2018
- Time
-
10:40 am - 11:30 am
- Event Category:
- Geometry and Topology Seminar