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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
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1572-9176
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Volume 26, Issue 2

Issues

On the construction of a covering map

Samson Saneblidze
  • Corresponding author
  • A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 6 Tamarashvili Str., Tbilisi 0177, Georgia
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Published Online: 2019-04-06 | DOI: https://doi.org/10.1515/gmj-2019-2016

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.

Keywords: Covering map; cubical set; necklical set

MSC 2010: 20F65; 57M10; 55U05; 55P35

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

References

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    M. Rivera and S. Saneblidze, A combinatorial model for the path fibration, J. Homotopy Relat. Struct. (2018), 10.1007/s40062-018-0216-4. Web of ScienceGoogle Scholar

About the article

Received: 2018-09-27

Accepted: 2018-12-28

Published Online: 2019-04-06

Published in Print: 2019-06-01


Funding Source: Shota Rustaveli National Science Foundation

Award identifier / Grant number: 217-614

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


Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 303–309, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2016.

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