On Belk's classifying space for Thompson's group F

@article{Sabalka2013OnBC,
  title={On Belk's classifying space for Thompson's group F},
  author={Lucas Sabalka and Matthew C. B. Zaremsky},
  journal={arXiv: Group Theory},
  year={2013}
}
The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to braids, except instead of braiding the strands split and merge. In Belk's thesis, a space CF was considered, of configurations of points on the real line allowing for splitting and merging, and a proof was sketched that CF is a classifying space for F. The idea there was to build the universal cover and construct an… 
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References

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