Homotopy | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-06

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Homotopy


00:00:48 1 Formal definition
00:02:24 1.1 Properties
00:03:12 2 Examples
00:05:12 3 Homotopy equivalence
00:06:01 3.1 Examples
00:07:37 3.2 Null-homotopy
00:08:25 4 Invariance
00:09:13 5 Variants
00:09:37 5.1 Relative homotopy
00:10:25 5.2 Isotopy
00:11:14 5.3 Timelike homotopy
00:12:02 6 Properties
00:12:50 6.1 Lifting and extension properties
00:13:38 6.2 Groups
00:14:26 6.3 Homotopy category
00:14:50 7 Applications
00:15:14 8 See also
00:16:02 9 References
00:16:51 10 Sources
00:17:39 Hn(g) : Hn(X) → Hn(Y) for all n.  Likewise, if X and Y are in addition path connected, and the homotopy between f and g is pointed, then the group homomorphisms induced by f and g on the level of homotopy groups are also the same: πn(f)
00:18:27 Applications
00:19:15 See also



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SUMMARY
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In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.In practice, there are technical difficulties in using homotopies with certain spaces.  Algebraic topologists work with compactly generated spaces, CW complexes, or spectra.