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On the construction of a covering map

  • Samson Saneblidze EMAIL logo
Published/Copyright: April 6, 2019
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Abstract

Let Y=|X| be the geometric realization of a path-connected simplicial set X, and let G=π1(X) be the fundamental group. Given a subgroup HG, let G/H be the set of cosets. Using the combinatorial model 𝛀X𝐏XX of the path fibration ΩYPYY and a canonical action μ:𝛀X×G/HG/H, we construct a covering map G/HYHY as the geometric realization of the associated short sequence G/H𝐏X×μG/HX. This construction, in particular, does not use the existence of a maximal tree in X. For a 2-dimensional X and H={1}, it can also be viewed as a simplicial approximation of a Cayley 2-complex of G.


Dedicated to Academician Nodar Berikashvili on the occasion of his 90th birthday


Award Identifier / Grant number: 217-614

Funding statement: This research was partially supported by Shota Rustaveli NSF grant 217-614.

References

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Received: 2018-09-27
Accepted: 2018-12-28
Published Online: 2019-04-06
Published in Print: 2019-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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