4-dimensional topology

4-Dimensional Topology

An online research community sponsored by the

 

American Institute of Mathematics, Pasadena, California

organized by

Miriam Kuzbary, Maggie Miller, Juanita Pinzón-Caicedo, and Hannah Schwartz

This research community, sponsored by AIM and the NSF, includes mathematicians at all career stages who study four-dimensional topology. Topology in dimension four uses different techniques than used in other dimensions: both high-dimensional surgery arguments and three-dimensional intuition typically fail in dimension four. Some interesting topics in this subfield include:

1. Understanding the difference between the topological and smooth categories in 4-dimensions.
2. Investigating surfaces embedded in 4-manifolds, which one can view as a higher dimensional analogue of classical knots.
3. Studying knots in 3-manifolds up to concordances in 4-manifolds.

This research community hosts small working groups and occasional seminars, as well as some regular social events such as virtual tea.

The primary goals of this research community are to:

1. Bring together expert and early-career researchers.
2. Simulate the spontaneous interactions of a mathematics department.
3. Spread awareness of cutting-edge research.
4. Increase the participation of young mathematicians in the broader math community.
5. Promote the research of and include mathematicians from underrepresented groups.

This program has concluded its activity.

For more information email research@aimath.org