(mathematics) A connection between two manifolds of the same dimension n. via a manifold of dimension n+1, where the smaller manifolds are included in the boundary of the larger manifold.
When cohomology became 'extraordinary' with the arrival of K-theory and cobordism theory from 1955 onwards, it was really only necessary to change the letter H everywhere to say what the characteristic classes were.
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Another part of Lurie's work is his article on topological field theories, where he sketches a classification of extended field theories using the language of infinity-categories (cobordism hypothesis).
His work on topology, in particular on characteristic classes, cobordism theory and the Thom transversality theorem led to his being awarded a Fields medal in 1958.
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Abstract. It is reviewed how the Khovanov homology is defined from a TQFT-functor between the category of $(1+1)-$cobordisms and the category of $R-$modules.
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