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Topology of smooth maps

Lecturer: 
Antonio Lerario
Course Type: 
PhD Course
Academic Year: 
2017-2018
Period: 
January-June
Duration: 
30 h
Description: 
The course will be an introduction to the notion of "generic" in differential topology.
We will study "generic" properties of function spaces between manifolds, i.e. properties shared by "most functions" -- this idea will be made rigorous. We will introduce the notion of regular value and prove Sard Lemma, then move to the core notion of transversality. We will prove the Jet-Transversality Theorem and discuss some of its applications. Time permitting, we will finish with some basic notions of Morse Theory.
 
The lectures will be based on the following books:
  • Hirsch, "Differential topology"
  • Milnor,  "Topology from the differentiable viewpoint"

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