Lefschetz fixed-point theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem


00:00:43 1 Formal statement
00:03:04 2 Sketch of a proof
00:04:16 3 Lefschetz–Hopf theorem
00:05:26 4 Relation to the Euler characteristic
00:06:35 5 Relation to the Brouwer fixed point theorem
00:07:31 6 Historical context
00:09:26 7 Frobenius
00:09:37 8 See also
00:15:31 9 Notes



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SUMMARY
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In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X to itself  by means of traces of the induced mappings on the homology groups of X. It is named after Solomon Lefschetz, who first stated it in 1926.
The counting is subject to an imputed multiplicity at a fixed point called the fixed point index. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle).