An Integral Graph Complex for Bordered Surfaces
نویسنده
چکیده
We define a category Fat whose objects are isomorphism classes of bordered fat graphs and show that its geometric realization is a classifying space for the bordered mapping class groups. We then construct a CW structure on this geometric realization with one cell per isomorphism classes of bordered fat graphs. Its cellular cochain complex gives a bordered graph complex which computes the integral cohomology of the bordered mapping class groups. We use this chain complex to compute the cohomology of the bordered mapping class group of a torus with a single boundary and to describe certain homological operations induced Miller’s double-loop structure.
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