UAM TOPOLOGY READING SEMINAR, we meet Fridays at 10:00 at room 420 at the Department of Mathematics.

FUNDAMENTAL GROUP

September 27th: Homotopy theory

October 4rd: Fundamental group

(pp. 21-37, 162-163 ; Ejercicios 0.1, 0.2, 0.16, 0.22, 0.23)

October 11th: The Seifert--Van Kampen theorem

October 12th: Proof of the Seifert--Van Kampen theorem

October 25th: Examples and exercises

November 8th: Covering spaces and their properties

November 15th: Classification of covering spaces

November 22st: Deck transformations

November 29th: Examples and exercises

December 13th: Classifying spaces of groups

HOMOLOGY

We will follow Chapters 6 and 7 from Randal-Williams's notes , together with Sheet 3 and Sheet 4.

February 24th: Sections 6.1 and 6.2. Exercises 3.1, 3.2, 3.3. (Federico Cantero)

March 3rd: Section 7.1. Exercises 3.4, 3.7 3.8. (Henrique Mendes)

March 10th: Sections 7.2 and 7.3. Exercises 3.5, 3.6 4.3. (Sergio Domingo)

March 17th: Section 7.4. Exercises 4.3, 4.4, 4.6. (Pablo Sánchez)

March 24th: Sections 7.5 and 7.6. Exercises 4.1, 4.7, 4.8 and this extra sheet (Rodrigo de Pool) - We'll meet at 9:30 to adapt to the unusual Colloquium schedule

March 31th: Problem session - We'll meet at 9:00 to adapt to the ICMAT distinguished lecture.

April 21st: Problem session.

April 28th: Section 7.8. Exercises 4.5, 4.9, 4.10, 4.11 (Sergio Domingo).

May 5th: Singular homology I. (Federico Cantero)

May 12th: Singular homology II. (Federico Cantero)

May 19th: Singular cohomology. (Federico Cantero)

May 26th: Group homology. (Federico Cantero)

Curiosidad: Ernesto Castro sobre la imposibilidad de la homología singular