Geometry and Topology (440-2-41)

Instructors

Allen Yuan

Meeting Info

Lunt Hall 101: Tues, Thurs 11:00AM - 12:20PM

Overview of class

The course will emphasize examples throughout the year. Winter (differentiable manifolds): differentiable manifolds; implicit function theorem and Sard's theorem; smooth vector bundles, tangent vectors, tensors, vector fields and flows. Lie derivatives, Lie groups and Lie algebras. Integral manifolds, Frobenius's theorem. Differential forms and the de Rham complex. Orientation, integration, Riemannian metrics, geodesics, exponential map. Spring (cohomology): de Rham cohomology, Mayer-Vietoris, Poincare' duality, singular homology and cohomology. Cohomolgy of cell complexes, simplicial cohomology, Cech cohomology. Cup product; sheaves. Prerequisites: MATH 440-1.

Class Materials (Required)

ISBN: 978-0521795401
Title: Algebraic Topology
Author: Allen Hatcher
Publisher: Cambridge University Press

Class Materials (Suggested)

No materials suggested. See required materials

Enrollment Requirements

Enrollment Requirements: Preregistration in this course is reserved for students who are majoring in Mathematics.