Math 215B: Differential Topology
Winter 2022
General information:
 Lectures: Tue, Th 9:45am 11:15am, room 384H. The first two weeks will be online, however the expectation is that the rest of quarter the Lectures will be in person.
 Professor: Eleny Ionel, office 383L,
ionel "at" math.stanford.edu
Office Hours: Th 2pm3pm and by appointment
 Course Assistant: Eric Kilgore, office 381N, ekilgore "at" stanford.edu
Office Hours: Tue and Wed 3pm4pm and by appointment

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.

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 other textbooks you will find useful:
M. Hirsch Differential Topology
J. Lee Introduction to Topological Manifolds
J. Milnor Morse Theory


Homework Policy:
Homework assignments are due each Thursday (unless otherwise noted). The lowest homework grade will be dropped. You are encouraged to discuss and work together on your homework, but everyone must write up their own solutions.