2 Matching Annotations
 Dec 2021

www.quantamagazine.org www.quantamagazine.org

Mathematicians already had a method, known as Morse theory, for studying these critical points.
Morse theory can be used to study critical points.

 Jun 2021

en.wikipedia.org en.wikipedia.org

To put it succinctly, differential topology studies structures on manifolds that, in a sense, have no interesting local structure. Differential geometry studies structures on manifolds that do have an interesting local (or sometimes even infinitesimal) structure.
Differential topology take a more global view and studies structures on manifolds that have no interesting local structure while differential geometry studies structures on manifolds that have interesting local structures.
