Path space (algebraic topology)
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In algebraic topology, a branch of mathematics, the based path space of a pointed space is the space that consists of all maps from the interval to X such that , called based paths.[1] In other words, it is the mapping space from to .
A space of all maps from to X, with no distinguished point for the start of the paths, is called the free path space of X.[2] The maps from to X are called free paths. The path space is then the pullback of along .[1]
The natural map is a fibration called the path space fibration.[3]
See also
[edit]References
[edit]- ^ a b Martin Frankland, Math 527 - Homotopy Theory - Fiber sequences
- ^ Davis & Kirk 2001, Definition 6.14.
- ^ Davis & Kirk 2001, Theorem 6.15. 2.
- Davis, James F.; Kirk, Paul (2001). Lecture Notes in Algebraic Topology (PDF). Graduate Studies in Mathematics. Vol. 35. Providence, RI: American Mathematical Society. pp. xvi+367. doi:10.1090/gsm/035. ISBN 0-8218-2160-1. MR 1841974.