Hyperbolic groups which fiber in infinitely many ways

Mecham, TaraLee; Mukherjee, Antara

doi:10.2140/agt.2009.9.2101

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Hyperbolic groups which fiber in infinitely many ways

TaraLee Mecham and Antara Mukherjee

Algebraic & Geometric Topology 9 (2009) 2101–2120

DOI: 10.2140/agt.2009.9.2101

Abstract

We construct examples of $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo class="qopname"> CAT</mo><mrow><mo class="MathClass-open">(</mo><mrow><mn>0</mn></mrow><mo class="MathClass-close">)</mo></mrow></math>$ , free-by-cyclic, hyperbolic groups which fiber in infinitely many ways over $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ℤ</mi></math>$ . The construction involves adding a specialized square 2–cell to a non-positively curved, squared 2–complex defined by labeled oriented graphs. The fundamental groups of the resulting complexes are $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo class="qopname"> CAT</mo><mrow><mo class="MathClass-open">(</mo><mrow><mn>0</mn></mrow><mo class="MathClass-close">)</mo></mrow></math>$ , hyperbolic, free-by-cyclic and can be mapped onto $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ℤ</mi></math>$ in infinitely many ways.

Keywords

hyperbolic groups, fibering

Mathematical Subject Classification 2000

Primary: 20F65

Secondary: 51H99

References

Publication

Received: 20 December 2008

Accepted: 26 July 2009

Published: 21 October 2009

Authors

TaraLee Mecham
Department of Mathematics College of Mount St. Joseph, 5701 Delhi Road Cincinnati, Ohio 45233-1670 USA

Antara Mukherjee
Department of Mathematics and Computer Science The Citadel, 171 Moultrie St. Charleston, SC 29409 USA

Volume 9, issue 4 (2009)