File:Covering-Graph.png
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![File:Covering-Graph.png](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Covering-Graph.png/800px-Covering-Graph.png?20190210214936)
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English: Example of the topological proof of the Nielsen-Schreier Theorem. The free group G = pi_1(X) has two generators corresponding to loops a,b from the base point P in X. The index 2 subgroup H of even-length words corresponds to the covering graph Y with two vertices corresponding to the cosets H and H' = aH = bH = a^{-1}H = b^{-1}H, and two lifted edges for each of the original loop-edges a,b. Contracting one of the edges of Y gives a homotopy equivalence to a bouquet of 3 circles, so that H = pi_1(Y) is free on three generators. |
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Author | Magyar25 |
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current | 21:49, 10 February 2019 | ![]() | 889 × 538 (15 KB) | Magyar25 (talk | contribs) | Cross-wiki upload from en.wikipedia.org |
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