Families of representations of punctured torus bundles (Q2757133)
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scientific article; zbMATH DE number 1675920
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Families of representations of punctured torus bundles |
scientific article; zbMATH DE number 1675920 |
Statements
19 June 2002
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torus bundle over the circle
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irreducible representation of fundamental group
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0.9290687
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0.90762293
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0.90558285
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0.89352834
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0.89278066
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0.88797534
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0.8848717
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0.88033044
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Families of representations of punctured torus bundles (English)
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\textit{B. Mangum} and \textit{P. Shanahan} [J. Knot Theory Ramifications 6, No. 6, 817-825 (1997; Zbl 0896.57007)] constructed a complex curve of irreducible \(SL(3,\mathbb C)\) representations of the fundamental group of a once punctured torus bundle over \(S^1\). In the present paper, following Mangum-Shanahan's recipe and using the Krammer representation of the braid group \(B_4\), a complex surface (2-parameter family) of irreducible \(SL(6,\mathbb C)\) representations of these fundamental groups is constructed (containing the curve of \(SL(3,\mathbb C)\) representations). As a corollary it is shown that almost all punctured torus bundle groups are linear. ``We hope that this complex surface contributes to an understanding of the geometry and topology of once punctured torus bundles''.
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