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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. |
| Date | |
| Source | Own work |
| Author | Magyar25 |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:49, 10 February 2019 | | 889 × 538 (15 KB) | Magyar25 | Cross-wiki upload from en.wikipedia.org |
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