In algebraic topology, a branch of mathematics, an approximate fibration is a sort of fibration such that the homotopy lifting property holds only approximately. The notion was introduced by Coram and Duvall in 1977.
A manifold approximate fibration is a proper approximate fibration between manifolds. Some authors believe that manifold approximate fibrations are the "correct bundle theory for topological manifolds and singular spaces".
- Hughes, C.B.; Taylor, L.R.; Williams, E.B. (July 1995). "Rigidity of fibrations over nonpositively curved manifolds". Topology. 34 (3): 565–574. doi:10.1016/0040-9383(94)00035-J.
Further reading
References
Coram, D.; Duvall, P. (1977). "Approximate fibrations". Rocky Mountain Journal of Mathematics. 7 (2): 275–288. doi:10.1216/RMJ-1977-7-2-275. https://doi.org/10.1216%2FRMJ-1977-7-2-275 ↩
Hughes, Taylor & Williams 1995, § 1. - Hughes, C.B.; Taylor, L.R.; Williams, E.B. (July 1995). "Rigidity of fibrations over nonpositively curved manifolds". Topology. 34 (3): 565–574. doi:10.1016/0040-9383(94)00035-J. https://doi.org/10.1016%2F0040-9383%2894%2900035-J ↩
Hughes, Taylor & Williams 1995, Introduction - Hughes, C.B.; Taylor, L.R.; Williams, E.B. (July 1995). "Rigidity of fibrations over nonpositively curved manifolds". Topology. 34 (3): 565–574. doi:10.1016/0040-9383(94)00035-J. https://doi.org/10.1016%2F0040-9383%2894%2900035-J ↩