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Orbits of braid groups on cacti

Orbits of braid groups on cacti
Orbits of braid groups on cacti
One of the consequences of the classification of finite simple groups is the fact that non-rigid polynomials (those with more than two finite critical values), considered as branched coverings of the sphere, have exactly three exceptional monodromy groups (one in degree 7, one in degree 13 and one in degree 15). By exceptional here we mean primitive and not equal to Sn or An, where n is the degree. Motivated by the problem of the topological classification of polynomials, a problem that goes back to 19th century researchers, we discuss several techniques for investigating orbits of braid groups on "cacti" (ordered sets of monodromy permutations). Applying these techniques, we provide a complete topological classification for the three exceptional cases mentioned above.
1609-4514
129-162
Jones, G.A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Zvonkin, A.
10e6e506-64a5-4d6e-802b-706a89baab05
Jones, G.A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Zvonkin, A.
10e6e506-64a5-4d6e-802b-706a89baab05

Jones, G.A. and Zvonkin, A. (2002) Orbits of braid groups on cacti. Moscow Mathematical Journal, 2 (1), 129-162.

Record type: Article

Abstract

One of the consequences of the classification of finite simple groups is the fact that non-rigid polynomials (those with more than two finite critical values), considered as branched coverings of the sphere, have exactly three exceptional monodromy groups (one in degree 7, one in degree 13 and one in degree 15). By exceptional here we mean primitive and not equal to Sn or An, where n is the degree. Motivated by the problem of the topological classification of polynomials, a problem that goes back to 19th century researchers, we discuss several techniques for investigating orbits of braid groups on "cacti" (ordered sets of monodromy permutations). Applying these techniques, we provide a complete topological classification for the three exceptional cases mentioned above.

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Published date: January 2002

Identifiers

Local EPrints ID: 41164
URI: http://eprints.soton.ac.uk/id/eprint/41164
ISSN: 1609-4514
PURE UUID: 54678699-1a63-45cd-a957-cc14f5ecd5bf

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Date deposited: 25 Jul 2006
Last modified: 15 Mar 2024 08:25

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Contributors

Author: G.A. Jones
Author: A. Zvonkin

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