Differential Topology I

MATH 7851.01: Differential Topology I

Whitney Immersion and Embedding Theorems, transverse functions, jet-bundles, Thom transversality; classification of vector bundles, collars, tubular neighborhoods, intersection theory; Morse functions and lemma; surgery, Smale cancellation.
Prereq: 6701 and 6801. Not open to students with credit for 7851.02.
Credit Hours

Recommended textbooks:

  • Differential Topology, by Hirsch, published by Springer, ISBN 9780387901480
  • Topology from the Differentiable Viewpoint, by Milnor, published by Princeton, ISBN 9780691048338
  • Differential Topology, 10th edition, by Guillemin & Pollack, published by AMS, ISBN 9780821851937