Smooth concordance classes of topologically slice knots

June 3 to June 7, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Shelly Harvey, JungHwan Park, and Arunima Ray

Original Announcement

This workshop will be devoted to the study of smooth concordance classes of topologically slice knots. Knot concordance provides a key tool to study the topology of manifolds in dimension three and four. The specific question of when a knot or link is slice is core to several problems in 4-manifold topology, from embeddings of surfaces to homology cobordisms between 3-manifolds. There are infinitely many topologically slice knots that are not smoothly slice, and each such knot gives rise to an exotic $R^4$.

The main topics for the workshop are:

  1. Filtrations of the knot concordance group, in particular, the bipolar filtration of the subgroup of topologically slice knots
  2. Metrics on the knot concordance group and the subgroup of topologically slice knots, both discrete and non-discrete metrics
  3. Operators acting on knot and link concordance
  4. Group properties of link concordance groups.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Branched covers bounding rational homology balls
by  Paolo Aceto, Jeffrey Meier, Allison N. Miller, Maggie Miller, JungHwan Park, András I. Stipsicz
Doubly slice knots and metabelian obstructions
by  Patrick Orson, Mark Powell
Embedding spheres in knot traces
by  Peter Feller, Allison N. Miller, Matthias Nagel, Patrick Orson, Mark Powell, Arunima Ray
Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
by  Stefan Friedl, Takahiro Kitayama, Lukas Lewark, Matthias Nagel, Mark Powell