September 2017 October 2017 |

4:00 pm Monday, October 16, 2017 Topology Seminar: Braids, gropes, Whitney towers, and solvability of linksby Shelly Harvey (Rice) in HBH 227- 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.
Submitted by neil.fullarton@rice.edu |