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 1977.1
A manifold approximate fibration is a proper approximate fibration between manifolds.2 Some authors believe that manifold approximate fibrations are the "correct bundle theory for topological manifolds and singular spaces".3
References
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.
- Hughes, Taylor & Williams 1995, § 1.
- 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.