for this workshop
Smooth concordance classes of topologically slice knots
American Institute of Mathematics, San Jose, California
Shelly Harvey, JungHwan Park, and Arunima Ray
This workshop, sponsored by AIM and the NSF, 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:
- Filtrations of the knot concordance group, in particular, the bipolar filtration of the subgroup of topologically slice knots
- Metrics on the knot concordance group and the subgroup of topologically slice knots, both discrete and non-discrete metrics
- Operators acting on knot and link concordance
- Group properties of link concordance groups.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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