Goodwillie's cosimplicial model for the space of long knots and its applications
Abstract
We work out the details of a correspondence observed by Goodwillie between cosimplicial spaces and good functors from a category of open subsets of the interval to the category of compactly generated weak Hausdorff spaces. Using this, we compute the first page of the integral Bousfield--Kan homotopy spectral sequence of the tower of fibrations given by the Taylor tower of the embedding functor associated to the space of long knots. Based on the methods in [Con08], we give a combinatorial interpretation of the differentials d1 mapping into the diagonal terms, by introducing the notion of (i, n)-marked unitrivalent graphs.
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