On h-fibrations

Year 2019, Volume: 48 Issue: 3, 732 - 742, 15.06.2019

Mehdi Tajik Behrooz Mashayekhy Ali Pakdaman

https://izlik.org/JA56JE89YJ

Abstract

In this paper, we study h-fibrations, a weak homotopical version of fibrations which have weak covering homotopy property. We present some homotopical analogue of the notions related to fibrations and characterize h-fibrations using them. Then we construct some new categories by h-fibrations and deduce some results in these categories such as the existence of products and coproducts.

Keywords

fiber homotopy , weak covering homotopy property , h-fibration , homotopically path lifting

References

• A. Dold, Partitions of unity in the theory of fibrations, Ann. Math. 78, 223-255, 1963.
• E. Fadell, On fibre spaces, Trans. Amer. Math. Soc 90, 1-14, 1959.
• K. Fuchs, Homotopiefaserungen, Dissertation, Universitat Saarbrucken.
• A. Hatcher, Algebraic topology, Cambridge University Press, 2001.
• P. Pavesic , A note on trivial fibrations, Glasnik Matematicki 46, 513-519, 2011.
• P. Pavesic and R.A. Piccinini, Fibrations and their classification, Heldermann, 2013.
• M. Tajik, B. Mashayekhy and A. Pakdaman, Unique path lifting from homotopy point of view, Acta Math. Vietnam. 43 (2), 257-273, 2018.
• E.H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.