TQFTs are a class of toy models for quantum gravity. When we look at the special case of 2-dimensional TQFTs we find a surprising connection with the world of abstract algebra. Namely, the category of commutative Frobenius algebras is equivalent to the category of 2d TQFTs. Under this equivalence, the "pair of pants" cobordism corresponds to multiplication.
*Corrections*
- At 05:00 The arrow coming from the unit cobordism should be pointing towards a map from k to H and not to just k itself. Alternatively the left of the arrow shouldn't be the unit cobordism, but the empty manifold.
This video is also a submission to the 3b1b Summer of Math Exposition contest (some.3b1b.co/)
Interested in how I made the video? You can find all the source files for the video here:
github.com/WannesMalfait/TQFTs
Made with:
Blender: www.blender.org/
Motion Canvas: motioncanvas.io/
Chapters:
00:00 - Intro
00:36 - Motivation from Physics
01:50 - TQFTs
02:36 - Cobordisms
05:27 - Frobenius Algebras
Social Media:
mathstodon.xyz/@WannesMalfait
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