Korean J. Math. Vol. 27 No. 2 (2019) pp.547-562
DOI: https://doi.org/10.11568/kjm.2019.27.2.547

Monodromy groupoid of a local topological group-groupoid

Main Article Content

Hürmet Fulya Akız

Abstract

In this paper, we define a local topological group-groupoid and prove that if $G$ is a local topological group-groupoid, then the monodromy groupoid $Mon(G)$ of $G$ is a local group-groupoid.



Article Details

References

[1] R. Brown, Topology and groupoids, Booksurge PLC (2006). Google Scholar

[2] R. Brown and O. Mucuk, Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115 (1994), 97–110. Google Scholar

[3] R. Brown and O. Mucuk, The monodromy groupoid of a Lie groupoid, Cah. Top. G eom. Diff. Cat. 36 (1995), 345-370. Google Scholar

[4] R. Brown and C. B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Konn. Ned. Akad. v. Wet. 79 (1976), 296–302. Google Scholar

[5] R. Brown and J. P. L.Hardy, Topological Groupoids I: Universal Constructions, Math. Nachr. 71 (1976), 273–286. Google Scholar

[6] Brown R., Danesh-Naruie, G. and Hardy J. P. L., Topological groupoids II: Covering morphisms and G-spaces, Math. Nachr. 74 (1976), 143–156. Google Scholar

[7] R. Brown, G. Danesh-Naruie, The Fundamental Groupoid as a Topological Groupoid, Proc. Edinb. Math. Soc. 19 (series 2), Part 3 (1975), 237–244. Google Scholar

[8] R. Brown, I ̇. I ̇ ̧cen and O. Mucuk, Holonomy and Monodromy Groupoids, Lie Algebroids, Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 54, (2001) 9–20. Google Scholar

[9] R. Brown, I ̇. I ̇ ̧cen and O. Mucuk, Local subgroupoids II: Examples and Properties, Topology and its Application 127 (2003), 393–408. Google Scholar

[10] C. Chevalley, Theory of Lie groups, Princeton University Press, 1946. Google Scholar

[11] L. Douady and M. Lazard, Espaces fibres en alg‘ebres de Lie et en groupes, Invent. Math. 1 (1966), 133–151. Google Scholar

[12] K.C.H. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Math. Soc. Lecture Note Series 124, Cambridge University Press, 1987. Google Scholar

[13] K.C.H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, London Math. Soc. Lecture Note Series 213, Cambridge University Press, 2005. Google Scholar

[14] O. Mucuk, B. Kılı ̧carslan, T. S ̧ahan and N. Alemdar, Group-groupoid and monodromy groupoid, Topology and its Applications 158 (2011), 2034–2042. Google Scholar

[15] O. Mucuk, Covering groups of non-connected topological groups and the mon- odromy groupoid of a topological groupoid, PhD Thesis, University of Wales, 1993. Google Scholar

[16] P.J. Olver, Non-associatibe local Lie groups, J. Lie Theory 6 (1996), 23–51. Google Scholar

[17] O. Mucuk, H. Y. Ay and B. Kılıc ̧arslan, Local group-groupoids, I ̇stanbul University Science Faculty the Journal of Mathematics 97 (2008). Google Scholar

[18] H. F. Akız, N. Alemdar, O. Mucuk and T. S ̧ahan, Coverings Of Internal Groupoids And Crossed Modules In The Category Of Groups With Operations, Georgian Mathematical Journal 20 (2013), 223–238. Google Scholar

[19] O. Mucuk and H.F Akız, Monodromy groupoid of an internal groupoid in topological groups with operations, Filomat 29 (10) (2015), 2355–2366. Google Scholar

[20] H. F. Akız, Covering Morphisms of Local Topological Group-Groupoids, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 88 (4) (2018). Google Scholar

[21] J. Pradines, Th eeorie de Lie pour les groupo ides diff erentiables, relation entre propri et es locales et globales, Comptes Rendus Acad. Sci. Paris, SYer A 263 (1966), 907-910. Google Scholar