Department of Mathematics

Geometry and Topology

  •  Shelly Harvey, Rice
  •  Pure braids and link concordance
  •  12/05/2019
  •  2:00 PM - 3:00 PM
  •  C304 Wells Hall

If one considers the set of m-component based links in R^3 with a 4-dimensional equivalence relationship on it, called concordance, one can form a group called the link concordance group, C^m. Questions in concordance are important in for classification questions in topological and smooth 4-manifolds It is well known that the link concordance group contains the isotopy class of pure braid with m strands, P_m. That is, two braids are concordant if and only if they are isotopic! In the late 90's Tim Cochran, Kent Orr, and Peter Teichner defined a filtration of the knot/link concordance group called the n-solvable filtration. This filtration gives a way to approximate whether a link is trivial in the group. We discuss the relationship between pure braids and the n-solvable filtration as well as various other more geometrically defined filtrations coming from gropes and Whitney towers. This is joint work with Aru Ray and Jung Hwan Park.



Department of Mathematics
Michigan State University
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