Vaughn Climenhaga

Associate Professor
Department of Mathematics
University of Houston

Math 7350

Geometry of Manifolds
Spring 2015

Announcement: The midterm exam will be Friday, March 13 during the regularly scheduled class time, and will cover all the material we have seen in lecture to that point.

Instructor: Vaughn Climenhaga
  • Office: 665 PGH
  • Office hours:  MWF 11-11:50am or by appointment 
  • Email: climenha [at]

Course information:
  • Lectures:  MWF, 10-10:50am, C 108
  • Textbook:  Introduction to Smooth Manifolds, second edition, by John M. Lee (Springer, 2013)
  • Course syllabus
This is the second part of the two-semester topology/geometry sequence that began with Math 6342.  We will study smooth manifolds and maps, tangent and cotangent vectors, and vector fields and bundles.  Further topics may include embeddings, Lie groups and algebras, tensors, differential forms, integration on manifolds, de Rham cohomology, flows, and distributions and foliations.


HW 1 (due Wed, Jan 28)
HW 2 (due Fri, Feb 6)
HW 3 (due Fri, Feb 20)
HW 4 (due Mon, Mar 2)
HW 5 (due Mon, Mar 9)
HW 6 (due Fri, Mar 27)
HW 7 (due Wed, Apr 8)
HW 8 (due Wed, Apr 22)
HW 9 (due Mon, May 4)

Other materials

Thomassen's paper on classification of surfaces

Review material for final exam