Chalk "Et j'espère que mes neveux me sauront gré, non seulement des choses que j'ai ici expliquées, mais aussi de celles que j'ai omises volontairement, afin de leur laisser le plaisir de les inventer."

René Descartes

This is the website for the course "Sheaves in Topology" (Master) in the summer semester 2023.

Content

This course will give an introduction to sheaves with some of their applications in topology. Topics covered will include: basic definitions and constructions, a brief introduction to homological algebra including the derived category, sheaf cohomology with examples, functoriality with base change, local and constructible sheaves; advanced topics like perverse sheaves and vanishing cycles will be considered if time permits.

As background I highly recommend a course in topology and some knowledge of homological algebra (we'll introduce most concepts from scratch, but quite quickly). A course in Algebraic topology is very useful, but could also be taken at the same time as this course.

The script and exercise sheets will be made available here for anybody who is interested.

If you are taking the course for credit you will also need to sign up on Stine.

Lectures

Lectures are scheduled for Tuesdays at 2.15pm in H4 and Friday at 12.15pm in H3, but I plan to move the second time slot tto 10.15am to avoid the clash with Algebraic Topology.

Classes

The second half of the Friday lecture will be used for an examples class where we discuss examples sheets and questions arising from lectures.

Notes

Lecture notes are available here. Please contact me with any comments or corrections!

Exercises

Example sheet 1.

Office hours

There are no official office hours planned. I will linger after all lectures to answer questions. You can also contact me by email!

Exam

There will be oral exams during the summer break.

To be admitted to the oral exam you should present solutions in the exercise class three times! There is no other requirement.