I have read (mainly in the articles of Atiyah) that the partition function is the simplest topological invariant of a quantum field theory.


I have an arithmetic geometry background and know statistical physics quite well, but am a beginner in QFT. A reference for details on the above statement in mathematical language à la "Quantum Fields and Strings: A Course for Mathematicians" would be highly appreciated.


A sketch of the ideas involved would be even nicer.


If this question is too simple or vague, please let me know - I will transfer it to SE.



Reference request: Partition function as a topological invariant of a QFT
This is one case where you might just want to go back to the original article that proved that a partition function is metric-independent and hence a topological invariant: Edward Witten, [Quantum field theory and the Jones polynomial](https://projecteuclid.org/euclid.cmp/1104178138) (1989) --- see page 361.


For a sketch of the idea, this [introduction](https://books.google.nl/books?id=jsvrvXPc4hIC&pg=PA25) by Marcos Marino seems useful (page 25+26).


