Introduction to Surgery Theory

• Selected topics in Topology, V5D1
• Master course
• Lecturer: Wolfgang Lück
• Winter term 20/21
• time : Tuesdays 10:15 - 12:00
• WS 20/21 : October 27th, 2020 - February 2th, 2021 except for December 29th, 2020 and January 5th, 2021
• SS 2021 : Apil 20th, 2021 - July 13th, 2021 except for May 25th, 2021
• place: online via ZOOM

Information about the concept of the course:

We are planning a kind of hybrid between a classical course and a reading course. Here you can find more information about this new concept. The idea is not to cover all details but to teach the participants how to read and absorb a manuscript without going through all details.

Participants

• Master students

• Phd-students

• Postdocs

• Advanced scientists which are not experts for surgery theory

Mathematicians from outside of Bonn are welcome and encouraged to participate.

Literature

The course will follow the draft of the book Surgery Theory: Foundations by Diarmuid Crowley, Tibor Macko and Wolfgang Lück. Our hope is to cover the first 11 chapters which are very close to their final form, but of course not in detail. The manuscript contains exercises with solutions.

Prerequisites

• Basics of algebraic topology (singular and cellular homology, Poincare duality, homotopy groups, Hurewicz and Whitehead Theorem, fibrations)

• Basics of differential topology (manifolds, vector bundles, tangent and normal bundle, fibre bundles, transversality, tubular neighbourhoods)

• Basics of algebra (rings, modules, chain complexes, groups, group rings)

Tutorial

We are planning an additional informal tutorial via ZOOM, where the participants can ask questions or require more information or explanations. It is planned for Thursdays starting at 16:00. The first one will be on October 29th, 2020. This event will not appear in the Vorlesungsverzeichnis (university calendar) and is completely voluntary. (There will be no Exercises.)

Information about access to the lecture and the tutorial via ZOOM can be found here

Blog

There will also be a blog, where the participants can post questions and answers or make suggestions or requests to the lecturer. We will use the Q&A platform PIAZZA. Information about it and how one can access it can be found here

Exams:

The final examinations in the summer term 2021 will take the form of an oral exam probably conducted via ZOOM for students in Bonn in the time period July 19th - 22th. The second batch of exams will be scheduled in the time period August 30th - September 3th

Recording of the lectures

We will post video recordings from each lecture, but not from the informal tutorial. The current recordings can be found here:

• lecture 01, October 27th, 2020 part 1 part 2
• lecture 02, November 3rd, 2020 part 1 part 2
• lecture 03, November 10th, 2020 part 1 part 2
• lecture 04, November 17th, 2020 part 1 part 2
• lecture 05, November 24th, 2020 part 1 part 2
• lecture 06, December 1rs, 2020 part 1 part 2
• lecture 07, December 8th, 2020 part 1 part 2
• lecture 08, December 15th, 2020 part 1 part 2
• lecture 09, December 22th, 2020 part 1 part 2
• lecture 10, January 12th, 2021 part 1 part 2
• lecture 11, January 19th, 2021 part 1 part 2
• lecture 12, January 26th, 2021 part 1 part 2
• lecture 13, February 2nd, 2021 part 1 part 2
• lecture 14, February 9th, 2021 part 1 part 2
• lecture 15, April 20th, 2021 part 1 + 2
• lecture 16, April 27th, 2021 part 1 part 2
• lecture 17, May 4th, 2021 part 1 part 2
• lecture 18, May 11th, 2021 part 1 part 2
• lecture 19, May 18th, 2021 part 1 part 2
• lecture 20, June 1rst, 2021 part 1 part 2
• lecture 21, June 8th, 2021 part 1 part 2 slides
• lecture 22, June 15th, 2021 part 1 part 2
• lecture 23, June 29th, 2021 part 1 part 2
• lecture 24, July 6th, 2021 part 1 part 2
• lecture 25, July 13th, 2021 part 1 part 2