---
date: 2021-10-21 18:42
modification date: Saturday 23rd October 2021 00:13:26
title: cobordism hypothesis
aliases: [cobordism hypothesis]

created: 2023-04-01T23:21
updated: 2023-04-01T23:22
---

Last modified date: <%+ tp.file.last_modified_date() %>


---

- Tags 
	- #higher-algebra 
- Refs:
	- Paper by Freed <https://arxiv.org/pdf/1210.5100.pdf#page=1>
	- Proof of the [cobordism hypothesis](Unsorted/cobordism%20hypothesis.md) <https://arxiv.org/pdf/0905.0465.pdf#page=1>
- Links:
	- [dualizable](Unsorted/dualizable.md)
	- [topological string theory](topological%20string%20theory)
	- [TQFT](Unsorted/TQFT.md)

---

# cobordism hypothesis

![](attachments/Pasted%20image%2020220730144904.png)

![](attachments/Pasted%20image%2020220529121705.png)

![](attachments/Pasted%20image%2020220429235946.png)

![](attachments/Pasted%20image%2020220413210213.png)
![](attachments/Pasted%20image%2020220413210229.png)

Requires 2-dualizability.

Determine a TFT...?

The cobordism hypothesis may be interpreted as the assertion that extended topological field theories are completely determined by the higher category formed by boundary conditions and their interfaces.
For example in two dimensions a topological gauge theory with gauge group G is determined by specifying the class of G-quantum mechanics that form boundary conditions, while in three dimensions we need to specify a class of two-dimensional field theories with G symmetry

![](attachments/Pasted%20image%2020220319211129.png)

![](2023-04-01-1.png)