Math 215B: Differential Topology

Winter 2023

Lectures: Tue, Th 9:00am- 10:20am, room 380F

Professor: Eleny Ionel, office 383L, ionel "at" math.stanford.edu

Course Assistant: Nikhil Pandit, 384L, npandit0 "at" stanford.edu

Course Description: This course is a graduate level course on differential topology, the second quarter of the Math 215 sequence. Topics covered include: Basics of differentiable manifolds (tangent spaces, vector fields, tensor fields, differential forms), embeddings, tubular neighborhoods, integration and Stokes' Theorem, deRham cohomology, intersection theory via Poincare duality, Morse theory.

For more details, see Course Outline.

Prerequisite: 215A or equivalent, along with a good understanding of multivariable calculus (inverse and implicit function theorems, uniqueness and existence results for ODE's, integration of multivariable functions), and point set and algebraic topology

Recommended References: We will not follow any textbook too closely, but a good reference for most of the material are Ralph Cohen's Lecture notes tentatively called "Bundles, Homotopy, and Manifolds" available online. Here are some textbooks you may find useful:

Homework Policy: Homework assignments are due each Thursday, unless otherwise noted. The lowest homework grade will be dropped.

Final Exam: Wednesday, March 22.