Mathematics 761
Differentiable Manifolds

  • Instructor: Gloria Mari Beffa
  • Office: Van Vleck Hall 309, ph: 263-1634.
  • Lectures: 2:30pm, Room B129 Van Vleck Hall.
  • Syllabus
  • Homework sets
  • Office hours: I will be in my office most of Tuesdays, Thursdays and Fridays. Either stop by or send me an e-mail to make an appointment.

    • Pinkall's f lat torus

    Pinkall's flat torus

    (In fact, this surface is not flat, but it is the conformal image of a flat torus lying in a four dimensional space)


    Overview


    This course is the first introduction to differentiable manifolds. We will cover the basics: differentiable manifolds, vector bundles, implicit function theorem, submersions and immersions, vector fields and flows, foliations and Frobenius theorem, differential forms and exterior calculus, integration and Stokes' theorem, De Rham theory, etc. If time allows it, we will branch into Riemannian manifolds. Prerequisites: Math 522 or equiv.

    Text

     "A Comprehensive Introduction to Differential Geometry, Vol. 1" by Michael Spivak. .

    Final Exam and midterms

    The first midterm will be October 13, in class, followed by take home (see syllabus).
    The second midterm will be November 17, in class, followed by take home.
    The final exam is to be announced.
    maribeff@math.wisc.edu