A Morse function is a generic map to the real line. A Morse 2-function is generic map to the plane, or other 2-manifold. These functions featured prominently in my dissertation where I used them to give a classification of 2D topological field theories in terms of generators and relations. Now David Gay and Robion Kirby are using them to study 4-manifolds.
- 4-manifold Abel Lecture algebraic K-theory axiomization calibrated geometry Cerf theory Clark Barwick cobordism hypothesis comparison problem Costello emily riehl Frobenius algebra generators and relations higher category theory homotopy category homotopy theory Mike Hopkins Morse 2-function ninja open-closed quantum field theory Stolz-Teichner symmetric monoidal bicategories topological conformal field theory topological field theories unicity Yasha Savelyev