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Strongly contracting geodesics in a tree of spaces

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Abstract

Let X be a tree of proper geodesic spaces with edge spaces strongly contracting and uniformly separated from each other by a number depending on the contraction function of edge spaces. Then we prove that the strongly contracting geodesics in vertex spaces are quasiconvex in X. We further prove that in X if all the vertex spaces are uniformly hyperbolic metric spaces, then X is a hyperbolic metric space and vertex spaces are quasiconvex in X.

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References

  1. Arzhantseva G N, Cashen C H, Gruber D and Hume D, Characterizations of Morse geodesics via superlinear divergence and sublinear contraction, Doc. Math. 22 (2017) 1193–1224

    MathSciNet  MATH  Google Scholar 

  2. Bestvina M and Feighn M, A combination theorem for negatively curved groups, J. Differ. Geom. 35 (1992) 85–101

    Article  MathSciNet  Google Scholar 

  3. Bridson M and Haefliger A, Metric Spaces of Non-Positive Curvature, Vol. 319 (1999) (Springer)

  4. Charney R and Sultan H, Contracting boundaries of CAT(0) spaces, J. Topol. 8(1) (2015) 93–117

    Article  MathSciNet  Google Scholar 

  5. Kapovich I, The combination theorem and quasiconvexity, Int. J. Algebra Comput. 11 (2001) 185

    Article  MathSciNet  Google Scholar 

  6. Szczepanski A, Relatively hyperbolic groups, Mich. Math. J. 45 (1998) 611–618

    Article  MathSciNet  Google Scholar 

  7. Sisto A, Quasi-convexity of hyperbolically embedded subgroups, Math. Z. 283 (2016) 649–658

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The research of the first author, Abhijit Pal was supported by INSPIRE Research Grant. The authors are thankful to the anonymous referee for his/her valuable comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208 016, India

    Abhijit Pal

  2. Department of Mathematics, Indian Institute of Science Education and Research, Bhopal, 462 066, India

    Suman Paul

Authors
  1. Abhijit Pal
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  2. Suman Paul
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Correspondence to Abhijit Pal.

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Communicated by Mahan Mj.

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Pal, A., Paul, S. Strongly contracting geodesics in a tree of spaces. Proc Math Sci 132, 29 (2022). https://doi.org/10.1007/s12044-022-00667-6

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  • DOI: https://doi.org/10.1007/s12044-022-00667-6

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