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Propagating quasiconvexity from fibers

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Abstract

Let \(1 \to K \to G\,\mathop \to \limits^\pi \,Q\) be an exact sequence of hyperbolic groups. Let Q1 < Q be a quasiconvex subgroup and let G1 = π−1(Q1). Under relatively mild conditions (e.g. if K is a closed surface group or a free group and Q is convex cocompact), we show that infinite index quasiconvex subgroups of G1 are quasiconvex in G. Related results are proven for metric bundles, developable complexes of groups and graphs of groups.

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Change history

  • 19 August 2022

    There is a corection on article title, instead of “fibersi” should be “fibers.”

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Acknowledgments

MM is supported by the Department of Atomic Energy, Government of India, under project no.12-R&D-TFR-14001. MM is also supported in part by a Department of Science and Technology JC Bose Fellowship, CEFIPRA project No. 5801-1, a SERB grant MTR/2017/000513, and an endowment of the Infosys Foundation via the Chandrasekharan-Infosys Virtual Centre for Random Geometry. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while MM participated in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester. PS was partially supported by DST INSPIRE grant DST/INSPIRE/04/2014/002236 and DST MATRICS grant MTR/2017/000485 of the Govt of India.

We are grateful to the anonymous referee for a careful reading of the manuscript and several helpful suggestions for improvement.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai, 400005, India

    Mahan Mj

  2. Department of Mathematical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, SAS Nagar, Punjab, Sector 81, 140306, India

    Pranab Sardar

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  1. Mahan Mj
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  2. Pranab Sardar
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Mj, M., Sardar, P. Propagating quasiconvexity from fibers. Isr. J. Math. 247, 923–953 (2022). https://doi.org/10.1007/s11856-021-2285-z

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  • DOI: https://doi.org/10.1007/s11856-021-2285-z

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