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.