Culler's algorithm for the group \(\text{SL}(2,\mathbb{Z})\) (Q2784969)
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scientific article; zbMATH DE number 1733187
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Culler's algorithm for the group \(\text{SL}(2,\mathbb{Z})\) |
scientific article; zbMATH DE number 1733187 |
Statements
24 April 2002
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commutator subgroups
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products of commutators
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fiberings
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Culler's algorithm for the group \(\text{SL}(2,\mathbb{Z})\) (English)
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A modification of \textit{M. Culler}'s algorithm [Topology 20, 133-145 (1981; Zbl 0452.20038)] is proposed to determine the minimal number of elements of the group \(\text{SL}(2,\mathbb{Z})\) required to represent an element from the commutator subgroup of \(\text{SL}(2,\mathbb{Z})\) as the product of their commutators. M.~Culler considered free groups and free products of finite groups. The problem for \(\text{SL}(2,\mathbb{Z})\) emerges in the investigation of fiberings by a torus over a two-dimensional oriented surface.
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