1,381 research outputs found

    Some properties of the theory of n-categories

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    Let LnL_n denote the Dwyer-Kan localization of the category of weak n-categories divided by the n-equivalences. We propose a list of properties that this simplicial category is likely to have, and conjecture that these properties characterize LnL_n up to equivalence. We show, using these properties, how to obtain the morphism n−1n-1-categories between two points in an object of LnL_n and how to obtain the composition map between the morphism objects

    The dual boundary complex of the SL2SL_2 character variety of a punctured sphere

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    Suppose C1,…,CkC_1,\ldots , C_k are generic conjugacy classes in SL2(C)SL_2({\mathbb C}). Consider the character variety of local systems on P1−{y1,…,yk}{\mathbb P}^1-\{ y_1,\ldots , y_k\} whose monodromy transformations around the punctures yiy_i are in the respective conjugacy classes CiC_i. We show that the dual boundary complex of this character variety is homotopy equivalent to a sphere of dimension 2(k−3)−12(k-3)-1
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