Homotopy groups and homotopy equivalence

Goal: Understand the basic notions of elementary homotopy theory.

Group Leader:  Paul Tudorache

Study Team: Paul Tudorache

Supervisor: Calin Lazaroiu

Scheme:

A. Basic theory of topological spaces. Homeomorphisms, strong homotopy
equivalence, deformation retracts.

B. The definition of based homotopy groups. Independence of basepoint
up to isomorphism.

C. The notion of weak homotopy equivalence.

D. Applications: Homotopy groups of spheres. Covering space theory.

Bonus: Basic theory of model categories, Quillen adjunction.

Historical: 50 min. presentation on the history of homotopy theory and the main contributors to its development.

References:

Munkres, "Topology"

Mac Lane, "Categories for the working mathematician"

May, "A concise course in algebraic topology"

May, "More concise algebraic topology"

Riehl, "Notes on Categorical Homotopy Theory"

More references here.