A New Agenda for Low-Dimensional Topology | Quanta Magazine

Abstraction: Creation of third Kirby problem list for low-dimensional topology

Key points:

• Rob Kirby published influential open-problem lists in 1978 (K1, ~80 problems) and 1997 (K2, 415 problems); K3 was assembled at AIM Pasadena in October 2023.
• K3 aims for ~400 problems and is a communal effort with 14 editors, unlike the earlier single-author lists.
• Solving a Kirby problem is career-defining: mentioned in recommendation letters, given to students after qualifying exams.
• New topics include Heegaard Floer homology (from Andreas Floer's 1990s work), the Schoenflies conjecture, and the smooth 4D Poincare conjecture.
• The field exploded 1981-1982 with Freedman's 4D Poincare proof, Thurston's geometrization conjecture, and Donaldson's work on 4-manifolds.

Connections: Rob Kirby · American Institute Of Mathematics · Low Dimensional Topology · Open Problem Lists · Manifolds

Source: https://www.quantamagazine.org/a-new-agenda-for-low-dimensional-topology-20240222/