We discuss the language of functorial field theories, i.e. symmetric monoidal functors on geometric bordism categories, starting with the relation of 1-dimensional Euclidean theories to quantum mechanics. We explain how their concordance classes can lead to generalized cohomology and how this extends to the twisted, equivariant cases.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/13069