Differential Topology

"Einstein himself regarded the abstract four-manifold as what remains of the 'ether' in general relativity... Perhaps we may say that in studying smooth manifolds we are studying the possible shapes of the ether." - R.W. Sharpe

Differential topology uses differential and integral calculus to study curves, surfaces, and their higher dimensional counterparts, collectively called smooth manifolds.

This is an advertisement for a guided reading seminar for the Spring 2022 semester on differential topology, with readings taken from:

  • Milnor, Topology from the Differentiable Viewpoint,

  • Guillemin and Pollack, Differential Topology,

  • Spivak, Calculus on Manifolds,

  • Penrose, The Road to Reality, and

  • Ueno, Shiga, and Morita, A Mathematical Gift.

We meet in Shineman 176, 4-5pm, on Fridays. All are welcome to attend.

A link to the seminar texts is here.