Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II

@article{Ellenberg2012HomologicalSF,
  title={Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II},
  author={Jordan S. Ellenberg and Akshay Venkatesh and Craig Westerland},
  journal={arXiv: Number Theory},
  year={2012}
}
We prove a version of the Cohen--Lenstra conjecture over function fields (completing the results of our prior paper). This is deduced from two more general theorems, one topological, one arithmetic: We compute the direct limit of homology, over puncture-stabilization, of spaces of maps from a punctured manifold to a fixed target; and we compute the Galois action on the set of stable components of Hurwitz schemes. 

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