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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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Construction of invariants of 4-manifolds with the Kirby calculus

Disclaimer: Shameless self-advertising. Yes, it can be done, and it's really beautiful! You can define the Crane-Yetter invariant with Kirby calculus, and possibly other TQFTs ("dichromatic model …
Manuel Bärenz's user avatar