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The homology of permutation racks

Abstract : Despite a blossoming of research activity on racks and their homology for over two decades, with a record of diverse applications to central parts of contemporary mathematics, there are still very few examples of racks whose homology has been fully calculated. In this paper, we compute the entire integral homology of all permutation racks. Our method of choice involves homotopical algebra, which was brought to bear on the homology of racks only recently. For our main result, we establish a spectral sequence, which reduces the problem to one in equivariant homology, and for which we show that it always degenerates. The blueprint given in this paper demonstrates the high potential for further exploitation of these techniques.
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Contributor : Victoria Lebed <>
Submitted on : Tuesday, October 27, 2020 - 2:40:27 PM
Last modification on : Tuesday, February 23, 2021 - 7:22:03 PM
Long-term archiving on: : Thursday, January 28, 2021 - 7:04:14 PM


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  • HAL Id : hal-02980406, version 1
  • ARXIV : 2011.04524



Victoria Lebed, Markus Szymik. The homology of permutation racks. 2020. ⟨hal-02980406⟩



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