Calculation of Bead Space Cohomology
نویسنده
چکیده
This paper describes one approach for calculating the cohomology of a particular complex which arises in knot theory and which is used to prove the existence of ‘associators’, a key ingredient in the construction of a universal knot invariant. The approach taken is to show that the relevant complex can be interpreted, essentially, as the cohomology of the functor Hom(K, C), where C is the coalgebra of commutative power series in a finite number of variables, and the Homs are bi-comodule morphisms from the ground field K into a cofree bi-comodule resolution of C. Techniques from homological algebra and Koszul duality theory are then used to compute this cohomology. The original content of this article consists only of the interpretation of the knot theory complex as the complex described above. Otherwise, the paper serves primarily to provide a description of the relevant homological and Koszul theoretic tools used.
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