1,368 research outputs found
The dual boundary complex of the character variety of a punctured sphere
Suppose are generic conjugacy classes in . Consider the character variety of local systems on whose monodromy transformations around the punctures
are in the respective conjugacy classes . We show that the dual boundary
complex of this character variety is homotopy equivalent to a sphere of
dimension
Some properties of the theory of n-categories
Let 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 up to equivalence. We show, using these
properties, how to obtain the morphism -categories between two points in
an object of and how to obtain the composition map between the morphism
objects
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