Algebraic Topology Schedule








A vague description of topics covered each class with tentative schedule:

Lecture 1: Topology background and Graphs



Lecture 2: Orientations on graphs, Cayley graphs and simplicial complexes



Lecture 3: More simplicial complexes



Lecture 4: Cell Complexes and homotopys of maps



Lecture 5: Homotopy equivalence of spaces



Lecture 6: The simplicial approximation theorem



Lecture 7: The fundamental group: Basics



Lecture 8: Functoriality of the fundamental group



Lecture 9: Edge loop group



Lecture 10: The fundamental group of the circle and the fundamental theorem of algebra



Lecture 11 and 12: Free groups, universal property, fundamental group of a graph and reduced words.



Lecture 13: Midterm/Review



Lecture 14: Group presentations: Basic properties



Lecture 15: Tietze Transformations



Lecture 16: Pushouts and Universal properties



Lecture 17: Proof of Seifert van Kampen Theorem



Lecture 18: Definition of covering spaces and several examples



Lecture 19: Lifting of maps to covering spaces, path lifting, uniqueness



Lecture 20



Lecture 21



Lecture 22



Lecture 23



Lecture 24



Lecture 25



Lecture 26