---
date: 2021-05-18
tags:
  - web/quick-notes
created: 2021-10-27T19:35
updated: 2024-04-19T16:16
---


# 2021-05-18

## Kristen Hendricks, Surgery formulas for involutive Heegaard Floer homology

Tags: 
#projects/notes/seminars #geomtop #geomtop/Floer-theory 
Refs:
[Heegard-Floer homology](Heegard-Floer%20homology.md)

> Reference: Kristen Hendricks, *Surgery formulas for involutive Heegaard Floer homology*. Stanford Topology Seminar.


- Want to study homology [cobordism groups](cobordism%20groups) of [3-manifolds](3-manifolds) $\Theta_\ZZ^3$.
  - We don't understand the torsion in this group.
  - Reduce to study of a group of "$\iota$ complexes".
  - **Theorem**: it has a $\ZZ^{\infty}$ summand.

- See [Seifert fibered spaces](Seifert%20fibered%20spaces).

- People like [HF](HF) because there are a lot of computational tools!
  In particular, a [surgery formula](surgery%20formula).


## 22:01

Check out [ideal sheaves](ideal%20sheaves), [Bridgeland stability conditions](Bridgeland%20stability%20conditions.md).

- "Rotate" an exact sequence to get an [exact triangle](exact%20triangle.md) :

  ![attachments/image_2021-05-18-22-20-05.png](attachments/image_2021-05-18-22-20-05.png)

  - Interpretation of the triangle: $F = E \ominus \OO(-n) = E \oplus \OO(-n)[1]$.
  - Interpret $\OO(-n)[1] = -\OO(n)$.

- What is an [etale algebra](etale%20algebra)?