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.

 

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Michigan State University
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