# Subdivisional spaces and graph braid groups

@article{An2017SubdivisionalSA, title={Subdivisional spaces and graph braid groups}, author={Byung Hee An and Gabriel C. Drummond-Cole and Ben Knudsen}, journal={arXiv: Algebraic Topology}, year={2017} }

We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we decompose $X$ and show that the homology of the configuration spaces of $X$ is computed by the derived tensor product of the Morse complexes of the pieces of the decomposition, an…

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