Surgery theory | Wikipedia audio article скачать в хорошем качестве

Surgery theory | Wikipedia audio article

This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Surgery... 00:01:28 1 Surgery on a manifold 00:02:10 1.1 Examples 00:08:50 1.2 Effects on homotopy groups, and comparison to cell-attachment 00:17:37 2 Application to classification of manifolds 00:20:02 2.1 The surgery approach 00:21:33 2.2 Structure sets and surgery exact sequence 00:26:13 3 See also 00:28:56 4 References Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: increases imagination and understanding improves your listening skills improves your own spoken accent learn while on the move reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services... Other Wikipedia audio articles at: https://www.youtube.com/results?searc... Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.8307104473527454 Voice name: en-US-Wavenet-B "I cannot teach anybody anything, I can only make them think." Socrates SUMMARY ======= In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by John Milnor (1961). Originally developed for differentiable (= smooth) manifolds, surgery techniques also apply to PL (= piecewise linear) and topological manifolds. Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along the cut or boundary. This is closely related to, but not identical with, handlebody decompositions. It is a major tool in the study and classification of manifolds of dimension greater than 3. More technically, the idea is to start with a well-understood manifold M and perform surgery on it to produce a manifold M ′ having some desired property, in such a way that the effects on the homology, homotopy groups, or other invariants of the manifold are known. The classification of exotic spheres by Michel Kervaire and Milnor (1963) led to the emergence of surgery theory as a major tool in high-dimensional topology.