Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 761: Differentiable Manifolds

Starting  in the academic year 2018-19, Math 761 will usually be offered in the spring semester.


Lu Wang, Fall 2016/2017:


  • Introduction to Smooth Manifolds, by John M. Lee.
  • Foundations of Differentiable Manifolds and Lie Groups, by Frank Warner.
  • A Comprehensive Introduction to Differential Geometry, Volume I, by Michael Sprivak.

Tentative Syllabus:

  • Differentiable manifold, differential map.
  • Tangent space, vector bundle.
  • Immersion and embedding.
  • Vector field, Lie derivative.
  • Frobenius Theorem.
  • Tensor and exterior algebra.
  • Integration, Stokes' Theorem.
  • De Rham cohomology, Poincare Lemma.
  • Sard's Theorem, degree of a map.
  • Mayer-Vietoris sequence for cohomology, Euler characteristic, triangulations, if time pertmitted.
Math 522 or equiv

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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