• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,345 answers , 22,720 comments
1,470 users with positive rep
818 active unimported users
More ...

  target category of extended field theory

+ 7 like - 0 dislike

For a topological field theory to be a true “extension” of an Atiyah-Segal theory, the top two levels of its target (ie its $(n-1)^{\text{st}}$ loop space) must look like $\text{Vect}$. What other (physical) considerations constrain the choice of target category? The targets of invertible field theories are (by definition) $\infty$-groupoids and (therefore) can be represented as spectra. What constraints can we impose on target spectra of invertible theories; in particular, on their homotopy groups?

This post imported from StackExchange Physics at 2014-08-03 09:26 (UCT), posted by SE-user user151696

asked Aug 2, 2014 in Theoretical Physics by user151696 (55 points) [ revision history ]
edited Aug 3, 2014 by Dilaton
What is the definition of TFT and the definiton of A-S theory you are using?

This post imported from StackExchange Physics at 2014-08-03 09:26 (UCT), posted by SE-user ACuriousMind
An A-S TFT is a functor from $\text{Bord}_{<n-1,n>}(\mathcal{F})$ to $\text{Vect}$ where $\mathcal{F}$ denotes a set of background fields, eg a spin structure. An extended theory is a functor from $\text{Bord}_n(\mathcal{F})$ to a symmetric monoidal $(\infty,n)$-category $\mathcal{C}$ that restricts to an A-S TFT on $(n-1)$- and $n$-manifolds.

This post imported from StackExchange Physics at 2014-08-03 09:26 (UCT), posted by SE-user user151696
Comment to the question (v2): Consider adding some references to make the question more accessible to a wider audience.

This post imported from StackExchange Physics at 2014-08-03 09:26 (UCT), posted by SE-user Qmechanic

10 years old question.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights