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Math 215B: Differential Topology

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Winter 2023

** Lectures:** Tue, Th 9:00am- 10:20am, room 380F
**Professor:** Eleny Ionel, office 383L, ionel "at" math.stanford.edu

**Office Hours:** Tuesday 2-3pm, Thursday 1-2pm and by appointment

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

**Office Hours:** Monday 2-3 pm, Wednesday 2-3 pm 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.

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:

- M. Hirsch, Differential Topology
- J. Lee, Introduction to smooth manifolds
- J. Milnor, Morse Theory

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

** Final Exam**: Wednesday, March 22.