Timeline for Freiheitssatz implies a finitely generated one relator group embeds in a two-generator one relator group?
Current License: CC BY-SA 3.0
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| Apr 19, 2011 at 22:23 | comment | added | JeremyKun | This is a very interesting proof! Unfortunately I am somewhat bound to use the Freiheitssatz in my exposition, but these stronger results are always interesting to note. Thank you! | |
| Apr 19, 2011 at 12:28 | history | edited | user6976 | CC BY-SA 3.0 |
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| Apr 19, 2011 at 12:13 | comment | added | user6976 | Andreas: There is only one edge (at most) between two vertices by definition of the graph (otherwise the classical result about planar graphs cannot be aplied). But every edge on the boundary of the subdiagram is shared by two subdiagrams or by the subdiagram and the boundary of $\Delta$. Each of these edges "realize" an edge of the auxiliary graph. | |
| Apr 19, 2011 at 7:56 | comment | added | Andreas Thom | Mark, I am lost at the point "... there exists a vertex of degree at most 5. Therefore either there are two subdiagrams ...". How do you conclude from an upper bound on the degree of a vertex a lower bound on the number of edges between two vertices? | |
| Apr 19, 2011 at 3:12 | history | edited | user6976 | CC BY-SA 3.0 |
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| Apr 19, 2011 at 2:42 | history | edited | user6976 | CC BY-SA 3.0 |
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| Apr 19, 2011 at 2:16 | history | answered | user6976 | CC BY-SA 3.0 |