# Algebraic Topology 1 (V4D1), WS 2023/34

Lecturer: Markus Hausmann (hausmann@math.uni-bonn.de)

Assistent: Elizabeth Tatum (tatum@math.uni-bonn.de)

### Lecture

Mondays, 14:15 - 16:00 and Fridays 14:15 - 16:00 in Kleiner Hörsaal, Wegelerstr. 10

** Topics **: Serre spectral sequence and applications (rational homotopy groups of spheres, cohomology of Eilenberg-MacLane spaces), Thom isomorphisms, characteristic classes, bordism theory.

** Prerequisites **: A good understanding of (co-)homology of spaces and some homotopy theory (e.g., Serre fibrations), as for example covered by the courses Topology I + II.

** Exam **: February 2nd, 2024, 14:00-16:00

** Reexam **: March 19th, 2024, 9:00-11:00, ** Kleiner HĂ¶rsaal. Please arrive at the lecture hall 10 minutes before the exam and bring a picture ID.**

The reexam review will take place on March 20th between 2-2:30pm, in the room 1.007 at the Mathematical Institute.

### Literature

Allen Hatcher: Spectral sequences in algebraic topology, available here: [Link]

Robert Mosher, Martin Tangora: Cohomology operations and applications in homotopy theory.

John McCleary: A User's guide to spectral sequences

John Milnor, James Stasheff: Characteristic classes

### Practice sheets

[Practice sheet 1]

[Practice sheet 2]

### Exercise sheets

[Homework 1]

[Homework 2]

[Homework 3]

[Homework 4]

[Homework 5 (with added finite type hypothesis in Problem 2)]

[Homework 6]

[Homework 7]

[Homework 8]

[Homework 9 (with incorrect first problem removed, see the explanation)]

[Homework 10]

[Homework 11]

## News

EMS Prize 2024 for Jessica Fintzen

Bonn mathematics performs excellently again in QS ranking

Stefan Schwede is invited speaker at the ECM 2024 in Sevilla

Jessica Fintzen wins Cole Prize

Regula Krapf receives university teaching award

Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts

Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019

Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023

Grants for Mathematics students from Ukraine

Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society

Peter Scholze elected as Foreign Member of the Royal Society