Geometriae Dedicata

, Volume 194, Issue 1, pp 99–129 | Cite as

Divergence spectra and Morse boundaries of relatively hyperbolic groups

  • Hung Cong TranEmail author
Original Paper


We introduce a new quasi-isometry invariant, called the divergence spectrum, to study finitely generated groups. We compare the concept of divergence spectrum with the other classical notions of divergence and we examine the divergence spectra of relatively hyperbolic groups. We show the existence of an infinite collection of right-angled Coxeter groups which all have exponential divergence but they all have different divergence spectra. We also study Morse boundaries of relatively hyperbolic groups and examine their connection with Bowditch boundaries.


Divergence spectra Morse boundaries Relatively hyperbolic groups 

Mathematics Subject Classification (2000)

20F67 20F65 



I would like to thank Prof. Ruth Charney for her suggestion to study the quasi-isometry invariant divergence spectra and her encouragement to publish this paper. I also thank Prof. Kim Ruane for helpful conversations about the connection between contracting boundaries and Bowditch boundaries that gave me motivation for studying Morse boundaries of relatively hyperbolic groups. I want to thank Prof. Christopher Hruska, Prof. Pallavi Dani, Hoang Thanh Nguyen and Kevin Schreve for their very helpful conversations and suggestions. I also thank the referee for advice that improved the exposition of the paper.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe University of GeorgiaAthensUSA

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