[Melissa Zhang]> Fall 2022 Seminar

Homotopy Types in Low-Dimensional Topology @ SLMath

We will be working through understanding the following papers:

(1) Lipshitz-Sarkar, A Khovanov Stable Homotopy Type

(2) Manolescu-Sarkar, A Knot Floer Stable Homotopy Type

Spacetime coordinates

Mondays, 1:30—3 pm (13:30—15:00) US Pacific Time
Simons Auditorium, SLMath

You can sign up to participate virtually here.

Schedule and References

Date Speaker Title / Subject Reference(s)
September 19 Melissa Zhang A framed flow category for the cube Section 4 of Lipshitz-Sarkar
September 26 Holt Bodish Non-Trivial Steenrod Squares on the Khovanov Homology of prime knots [H. Bodish] Non-Trivial Steenrod Squares on the Khovanov Homology of prime knots
[Lawson-Lipshitz-Sarkar] Khovanov homotopy type, Burnside category, and products
October 3 Siyang Liu Khovanov homology via resolution configurations Section 2 of Lipshitz-Sarkar
October 10 No seminar — Indigenous Peoples Day
October 17 Inbar Klang The Cohen-Jones-Segal construction
October 24 No seminar — Workshop
October 31 No seminar because Melissa was too busy!
November 7 Melissa Zhang Lipshitz-Sarkar's Khovanov framed flow category Section 5 of Lipshitz-Sarkar
November 14 No seminar — Workshop
November 21 Jesse Cohen Grid complexes; obstruction classes, the complex of positive domains with partitions Sections 2, 3, and 4 of Manolescu-Sarkar
November 28 Kristen Hendricks Stratified spaces, Whitney umbrella and generalizations Sections 6 and 7 of Manolescu-Sarkar
December 5 Melissa Zhang The stratified spaces M(N, λ) modeling moduli spaces Sections 8 and 9 of Manolescu-Sarkar
December 12 Akram Alishahi Inductive construction of the HFK moduli spaces Section 12 of Manolescu-Sarkar
December 19 (Overflow date)

Potentially Open Problems

Here, I might keep track of open problems that come up during the seminar.

Papers related to the Lipshitz-Sarkar Khovanov stable homotopy type:

I'm collecting a list of papers written about the Khovanov and Knot Floer stable homotopy types in order to get a sense of what ideas have been explored already, and who the explorers are.

A lot of work has been done in the past decade, and I am trying to keep this list somewhat focused. I am only listing papers that work with either the framed-flow-category or Burnside-functor constructions. If your paper should be on this list, please contact me.

It takes me ten times longer to add links for papers, so no links shall be provided.

First of all, check out:


Working with flow categories:

The Burnside functor construction:

Stable homotopy types for Khovanov-like homologies:

Cobordisms between links:

Group actions:

Steenrod operations: