Schedule

This semester schedule is from Andrew Snowden’s Undergraduate Seminar in Topology at MIT.

February

W 	Feb 2 	Andrew 	Organizational meeting
F 	Feb 4 	Andrew 	Introduction to the fundamental group
M 	Feb 7 	Scott 	Paths and homotopies
		Umut 	The fundamental group
W 	Feb 9 	Kyle 	The fundamental group of the circle
		JJ 	Applications of previous lecture
F 	Feb 11 	Marcel 	Contractible and simply connected spaces
		Danny 	The fundamental group of a product
M 	Feb 14 	John 	Functoriality of the fundamental group
		Noah 	Homotopy equivalences
W 	Feb 16 	Rafael 	The fundamental group of S1 ∨ S1
		Gabriel Amalgamated free products
F 	Feb 18 	Aldo 	van Kampen's theorem
		Andrew 	van Kampen's theorem (continued)
M 	Feb 21 	President's Day, no class. But there is class tomorrow.
T 	Feb 22 	Andrew 	Introduction to covering spaces
W 	Feb 23 	Rafael 	The universal cover
		JJ 	The universal cover (continued)
F 	Feb 25 	Noah 	Lifting properties 	pdf
		Gabriel Lifting properties (continued)
M 	Feb 28 	Danny 	Existence of covers
		Umut 	The Galois correspondence

March

W 	Mar 2 	Kyle 	Category theory
		Marcel 	The Galois correspondence in categorical form
F 	Mar 4 	John 	Covering spaces of S1 ∨ S1
		Aldo 	Quotients by finite groups
M 	Mar 7 	Andrew 	Overview of homology
W 	Mar 9 	Scott 	Chains and the boundary operator
		Noah 	Definition of homology and first calculations
F 	Mar 11 	John 	Chain complexes
		Rafael 	Functoriality of homology
M 	Mar 14 	Aldo 	The long exact sequence
		Danny 	Relative homology
W 	Mar 16 	Scott 	Excision
		JJ 	Homology of a quotient
F 	Mar 18 	Umut 	Proof of Prop. 2.21, part 1
		Gabriel Proof of Prop. 2.21, part 2
M 	Mar 21 	Spring break, no class.
W 	Mar 23 	Spring break, no class.
F 	Mar 25 	Spring break, no class.
M 	Mar 28 	Andrew 	Review
		Andrew 	Naturality of connecting homomorphisms
W 	Mar 30 	Kyle 	Axioms for homology
		Rafael 	The Mayer–Vietoris sequence

April

F 	Apr 1 	Andrew 	Homology with coefficients
		Danny 	The universal coefficient theorem
M 	Apr 4 	Noah 	CW complexes, part 1
		Umut 	CW complexes, part 2
W 	Apr 6 	JJ 	CW homology, part 1
		Scott 	CW homology, part 2
F 	Apr 8 	Aldo 	Definition of cohomology
		Kyle 	Overview of formal properties
M 	Apr 11 	John 	The cup product, part 1
		Gabriel The cup product, part 2
W 	Apr 13 	Umut 	The Kunneth formula, part 1
		Andrew 	The Kunneth formula, part 2
F 	Apr 15 	Andrew 	Overview of Poincare duality
		Kyle 	Orientations
M 	Apr 18 	Patriot's Day, no class.
W 	Apr 20 	JJ 	The fundamental class, part 1
		Rafael 	The fundamental class, part 2
F 	Apr 22 	Andrew 	Direct limits
		Scott 	Cohomology with compact support
M 	Apr 25 	Aldo 	The cap product
		Danny 	Statement of Poincare duality
W 	Apr 27 	John 	Proof of Lemma 3.36
		Noah 	Proof of Poincare duality
F 	Apr 29 	Andrew 	Closing lecture

May

M 	May 2 	John 	Sheaf cohomology
		Noah 	Morse theory
W 	May 4 	JJ 	Hopf fibrations
		Aldo 	The Gauss—Bonnet theorem
F 	May 6 	Scott 	K-theory
		Umut 	De Rham cohomology
M 	May 9 	Danny 	The Hurewicz isomorphism
		Rafael 	Orbifold fundamental groups
W 	May 11 	Kyle 	Simplicial sets
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