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Lefschetz pencils and
finitely presented groups
Ryoma Kobayashi and Naoyuki Monden |
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Vol. 282 (2016), No. 2, 359–388
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Abstract |
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From the works of Gompf and Donaldson, it is known that every finitely presented group can be realized as the fundamental group of the total space of a Lefschetz pencil. We give an alternative proof of this fact by providing the monodromy explicitly. In the proof, we give an alternative construction of the monodromy of Gurtas’ fibration and a lift of that to the mapping class group of a surface with two boundary components. |
Keywords
Lefschetz pencil, Lefschetz fibration, fundamental group,
mapping class group
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Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 20F34
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Milestones
Received: 27 March 2015
Revised: 22 September 2015
Accepted: 30 September 2015
Published: 3 March 2016
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Authors |
| Ryoma Kobayashi | |
| Department of General
Education Ishikawa National College of Technology Tsubata, Ishikawa 929-0392 Japan |
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| Naoyuki Monden | |
| Department of Engineering
Science Osaka Electro-Communication University Hatsu-cho 18-8 Neyagawa 572-8530 Japan |
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