ACTIONS AND COVERINGS OF TOPOLOGICAL GROUPOIDS

Year 2013, Volume: 1 Issue: 2, 72 - 83, 01.12.2013

A.fatih Özcan

Abstract

Let R be a topological group-groupoid.We define a categoryT GGdCov(R) of coverings of R and a category T GGdOp(R) of actions of R ontopological groups and then prove the equivalence of these categories. Further,if R is topological ring-groupoid then we define a category T RGdCov(R) ofcoverings of R and a category T RGdOp(R) of actions of R on topological ringsand then prove the equivalence of these categories

Keywords

Topological coverings, topological group-groupoids, topological ringgroupoids, actions

References

• Brown, R., Topology and Groupoids, Booksurge LLC, 2006.
• Brown, R. and Danesh-Naruie, G., The Fundamental Groupoid as a Topological Groupoid, Proc. Edinb. Math. Soc., (1975), Vol. 19, (series 2), Part 3, 237-244.
• Brown, R., Danesh-Naruie, G. and Hardy, J. P. L., Topological groupoids II: Covering mor- phisms and G-spaces, Math. Nachr., (1976), 74: 143-145.
• Brown, R., ˙I¸cen, ˙I. and Mucuk, O., Holonomy and Monodromy Groupoids, Banach Center Publ.Polish Acad. Sci., Warsaw(2001), Vol.54, 9-20.
• Brown, R. and Mucuk, O., Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc., (1994), 115: 97-110.
• Gabriel, P. and Zisman, M., Categories of Fractions and Homotopy Theory, Springer-Verlag, Heidelberg, (1967).
• Hardy, J. P. L., Topological groupoids: Coverings and Universal Constructions, PhD Thesis, University College of North Wales, (1974).
• ˙I¸cen, ˙I. and ¨Ozcan, A.F., Topological Crossed Modules and G-groupoids, Algebras Groups Geom., (2001), 18: 401-410.
• ˙I¸cen, ˙I., ¨Ozcan, A.F. and G¨ursoy, M.H., Topological Group-groupoids and Their Coverings, Indian J. Pure Appl. Math., (2005), 36(9): 493-502.
• Mackenzie, K. C. H., General Theory of Lie Groupoids and Lie Algebroids, New York: Cam- bridge University Press, (2005).
• Mucuk, O., Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid, PhD Thesis, University of Wales England, (1993).
• Mucuk, O., Coverings and Ring-Groupoids, Georgian Math. J., (1998), Vol:5, 5:475-482.
• Mucuk, O. and ˙I¸cen, ˙I., Coverings of Groupoids, Hadronic J. Suppl., (2001) 16: 183-96.
• ¨Ozcan, A.F., ˙I¸cen, ˙I. and G¨ursoy, M.H., Topological Ring-groupoids and Liftings, Iran. J. of Sci. Technol. Trans. A., (2006), Vol.30, 355-362.
• ˙In¨on¨u University-Science and Art Faculty, Department of Mathematics, Malatya, Turkey, E-mail address: [e-mail]