Topology Seminar

Wednesday, October 4, 2017
4:20 PM - 5:20 PM (ET)
Exley Science Center Tower ESC 638
Event Type
Canalia, Caryn

Speaker: Shelly Harvey, Rice University

Title: Braids, gropes, Whitney towers, and solvability of links

 Abstract: The n-solvable filtrations of the knot/link concordance groups were defined as a way of studying the structure of the groups and in particular, the subgroup of algebraically slice knots/links.  While the knot concordance group C^1 is known to be an abelian group, when m is at least 2, the link concordance group C^m of m-component (string) links is known to be non-abelian.  In particular, it is well known that the pure braid group with m strings is a subgroup of C^m and hence when m is at least 3, this shows that C^m contains a non-abelian free subgroup.  We study the relationship between the derived subgroups of the the pure braid group, n-solvable filtration of C^m, links bounding symmetric Whitney towers, and links bounding gropes.  This is joint with with Jung Hwan Park and Arunima Ray.

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