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}
}
  • Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
  • Published 2017
  • Mathematics
  • arXiv: Algebraic Topology
  • 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… CONTINUE READING
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