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Allison Miller, UT Austin, Winding number of satellite operators and concordance

February 21, 2018 | 10:40 am - 11:30 am EST

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 EST
Event Category:

Venue

SAS 4201