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MONODROMY GROUPOID OF A LOCAL TOPOLOGICAL GROUP-GROUPOID

  • Akiz, H. Fulya (Department of Mathematics Yozgat Bozok University)
  • Received : 2019.04.08
  • Accepted : 2019.06.20
  • Published : 2019.06.30

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.

Keywords

References

  1. R. Brown, Topology and groupoids, Booksurge PLC (2006).
  2. R. Brown and O. Mucuk, Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115 (1994), 97-110. https://doi.org/10.1017/S0305004100071942
  3. R. Brown and O. Mucuk, The monodromy groupoid of a Lie groupoid, Cah. Top. Geom. Diff. Cat. 36 (1995), 345-370.
  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.
  5. R. Brown and J. P. L.Hardy, Topological Groupoids I: Universal Constructions, Math. Nachr. 71 (1976), 273-286. https://doi.org/10.1002/mana.19760710123
  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. https://doi.org/10.1002/mana.3210740110
  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. https://doi.org/10.1017/S0013091500015509
  8. R. Brown, I. Icen and O. Mucuk, Holonomy and Monodromy Groupoids, Lie Algebroids, Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 54, (2001) 9-20.
  9. R. Brown, I. Icen and O. Mucuk, Local subgroupoids II: Examples and Properties, Topology and its Application 127 (2003), 393-408. https://doi.org/10.1016/S0166-8641(02)00101-3
  10. C. Chevalley, Theory of Lie groups, Princeton University Press, 1946.
  11. L. Douady and M. Lazard, Espaces fibres en alg'ebres de Lie et en groupes, Invent. Math. 1 (1966), 133-151. https://doi.org/10.1007/BF01389725
  12. K.C.H. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Math. Soc. Lecture Note Series 124, Cambridge University Press, 1987.
  13. K.C.H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, London Math. Soc. Lecture Note Series 213, Cambridge University Press, 2005.
  14. O. Mucuk, B. Kilicarslan, T. Sahan and N. Alemdar, Group-groupoid and monodromy groupoid, Topology and its Applications 158 (2011), 2034-2042. https://doi.org/10.1016/j.topol.2011.06.048
  15. O. Mucuk, Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid, PhD Thesis, University of Wales, 1993.
  16. P.J. Olver, Non-associatibe local Lie groups, J. Lie Theory 6 (1996), 23-51.
  17. O. Mucuk, H. Y. Ay and B. Kilicarslan, Local group-groupoids, Istanbul University Science Faculty the Journal of Mathematics 97 (2008).
  18. H. F. Akiz, N. Alemdar, O. Mucuk and T. Sahan, Coverings Of Internal Groupoids And Crossed Modules In The Category Of Groups With Operations, Georgian Mathematical Journal 20 (2013), 223-238.
  19. O. Mucuk and H.F Akiz, Monodromy groupoid of an internal groupoid in topological groups with operations, Filomat 29 (10) (2015), 2355-2366. https://doi.org/10.2298/FIL1510355M
  20. H. F. Akiz, Covering Morphisms of Local Topological Group-Groupoids, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 88 (4) (2018).
  21. J. Pradines, Theeorie de Lie pour les groupoides differentiables, relation entre proprietes locales et globales, Comptes Rendus Acad. Sci. Paris, SYer A 263 (1966), 907-910.