Math 132: Differential Topology (Spring 2026)

Meeting time and location:

Tue Thu 9:00 AM - 10:15 AM at Science Center TBD.

Instructor:

Sunghyuk Park
Email: sunghyukpark at math dot harvard dot edu
Office hours: TBD at Science Center 231

Course goals:

This course is an introduction to the topology of smooth manifolds and smooth maps, from the perspective of oriented intersection theory.
Here are the topics I am planning to talk about:

• Smooth manifolds and smooth maps
• Transversality, mod 2 intersection theory, winding numbers, Jordan-Brouwer separation theorem, Borsuk-Ulam theorem
• Oriented intersection theory, Lefschetz fixed point theorem, vector fields, index and degree, Poincare-Hopf theorem, Euler characteristic
• Differential forms, integration, de Rham cohomology, Stokes theorem, Gauss-Bonnet theorem

Textbook:

Guillemin & Pollack - Differential Topology [pdf]

Recommended Prep:

Mathematics 22a,b, 23a,b or 25a,b or 55a,b or 112; or an equivalent background in mathematics.

Harvard College Honor Code:

"Members of the Harvard College community commit themselves to producing academic work of integrity – that is, work that adheres to the scholarly and intellectual standards of accurate attribution of sources, appropriate collection and use of data, and transparent acknowledgement of the contribution of others to their ideas, discoveries, interpretations, and conclusions. Cheating on exams or problem sets, plagiarizing or misrepresenting the ideas or language of someone else as one's own, falsifying data, or any other instance of academic dishonesty violates the standards of our community, as well as the standards of the wider world of learning and affairs."