Meetings:
We will follow Nikolai Saveliev's book "Lectures on the Topology of 3-manifolds", covering major topics like Heegaard splittings, Dehn surgery, Kirby calculus, intersection forms of 4-manifolds, invariants of knots and links, and fibered knots.
Here is the publisher's page: [book]
(You should check the library for a copy first.)
On Thursday, January 23rd, I will need to join the meeting on Zoom. I'll send out a Zoom link. You all can organize/choose whether to gather in-person or on Zoom.
The topics/breakdown are subject to change.
There are many good exercises in the book. You should try them to check your understanding of each chapter.
| Date | Speaker | Proposed Topic (subject to change) |
|---|---|---|
| 1/16 | Melissa Zhang | Ch 1, Heegaard splittings and diagrams:
gluing construction, boundary orientation, smooth/top concerns; handlebodies, triangulations; Heegaard diagrams, preliminary examples (S3, S1xS2, T3, maybe RP3); crash course in Morse theory and handlebody theory in 3D (not in the book) |
| 1/23 | Annette Belleman | (Melissa will be on Zoom)
Ch 1, Examples: genus 0, Alexander trick; genus 1, framing on torus, setting conventions (in preparation for Dehn surgery), computing fundamental group; |
| 1/30 | Wren Burrill | Ch 2, Dehn surgery:
surgery on links, Lickorish-Wallace theorem; lens space and Seifert fibered space examples; surgery and 4-manifolds |
| 2/6 | Ella Curtiss | Dehn surgery continued |
| 2/13 | Wren Burrill | (Melissa wasn't there; topics that follow comprise the original suggestion)
Ch 3, Kirby calculus: linking number, Kirby moves; linking matrix (for use later in comparison with intersection form) There are a lot of tricks here to get used to, so any extra time should be spent on working useful examples. |
| 2/20 | (cancelled) | |
| 2/27 | Annette Belleman | (Melissa isn't sure what the intended topic is yet) Ch 5, 4-manifolds:
intersection form, properties that relate to topology (e.g. unimodularity) and Kirby calculus; don't get bogged down on deep algebraic topology / gauge theory and stick to the topology + linear algebra |
| 3/5 and 3/6 | Trevor on Wed, informal discussion on Thurs | See forthcoming email from Trevor about student-run topology seminar Wed 4-5 pm. On Thursday at our usual time, we'll have an informal discussion about any topics people want to go over again, or possibly a topic Melissa thinks we should talk about. |
| 3/13 | Chris Luevano | Ch 7, Seifert surfaces:
Seifert surfaces, Seifert matrix, S-equivalence, intersection form; Alexander polynomial for knots |