Announcements

• The final exam will take place on April 25, from 9:00am to 12:00am, in Amphi A.
• The midterm exam will take place on February 28, from 8:00am to 10:00am, in Amphi A.
• On Monday, February 6, we will have a tutorial at the usual scheduled time 8:00am, and we will also have an extra lecture from 5:00pm to 7:00pm in room 435.
• On Monday, January 30, we will have a tutorial at the usual scheduled time 8:00am, and we will also have an extra lecture from 5:00pm to 7:00pm in room 435.
• The lecture of January 16 and the tutorial of Tuesday January 17 are canceled.
• All the students attending the course should subscribe to it in the portail des études.

Schedule

• Lectures (Marco Mazzucchelli) : Tuesday 8:00am - 10:00am, Amphi A
• Tutorials (Raphaël Ruimy) : Monday 8:00am - 10:00am, room A1

Calendar (lectures, tutorials)

January 9:	Introduction Recap of general topology Fundamental group Brower's fixed point theorem in dimension 2 Theorem of the invariance of domain in dimension 2 Introduction to higher homotopy groups
January 10:	Exercises:
January 16:	Canceled
January 17:	Canceled
January 23:	Exercises: Solutions:
January 24:	Singular homology Hurewicz theorem
January 30:	Exercises:
January 30:	(extra lecture, from 5:00pm to 7:00pm, room 435) Homology homomorphisms induced by continuous maps Homotopy invariance of singular homology Short and long exact sequences of chain complexes Relative homology
January 31:	Subdivision homomorphism Theorem of small chains Excision Mayer-Vietoris long exact sequence
February 6:	Exercises:
February 6:	(extra lecture, from 5:00pm to 7:00pm, room 435) Homology of spheres Local homology Theorem of the invariance of domain Brower's fixed point theorem Topological degree Hairy ball theorem CW complexes
February 7:	CW decomposition of spheres and projective spaces Cellular homology theorem
February 20:	Exercises:
February 21:	Homology of quotients and wedge sums Boundary homomorphism in cellular homology Homology of real projective spaces Euler characteristic
March 6:	Exercises:
March 7:	Singular homology with coefficients Singular cohomology Free resolutions
March 13:	Exercises:
March 14:	Proof of the universal coefficient theorem
March 20:	Exercises:
March 21:	Cup product Crossed cup product Künneth theorem
March 27:	Exercises:
March 28:	Orientability of topological manifolds Fundamental class
April 3:	Exercises:
April 4:	Cohomology with compact support Cap product Poincaré duality
April 17:	Exercises:
April 18:	Exercises: