Carolyn R. Abbott
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Published Papers:
  1. Not all finitely generated groups have universal acylindrical actions. Proc. Amer. Math. Soc., 144(10):4151–4155, 2016, pdf.
  2. (with F. Dahmani) Acylindrically hyperbolic groups have property P_naive. arXiv:1610.04143.  Math. Z., 291(1-2):555-568, 2019.
  3. (with S. Balasubramanya and D. Osin) Hyperbolic structures on groups.  arXiv:1710.05197. Algebr. Geom. Topol., 19-4, 1747-1835, 2019.
  4. (with D. Hume and D. Osin) Extending group actions on metric spaces.   arXiv:1703.03010.  J. Topol. Anal., 12(3): 625--665, 2020, pdf.
  5. (with D. Hume) The geometry of generalized loxodromic elements.  arXiv:1802.03089.  Ann. I. Fourier (Grenoble), 70(4): 1689--1713, 2020.
  6. (with J. Behrstock and M. Durham) Largest acylindrical actions and stability in hierarchically hyperbolic groups, with an appendix by Daniel Berlyne and Jacob Russell. arXiv:1705.06219. Trans. Amer. Math. Soc. Ser. B, 8: 66--104, 2021 
  7. (with D. Hume) Actions of small cancellation groups on hyperbolic spaces.  arXiv:1807.10524. ​Geom. Dedicata, 212(1), 325--363, 2021.
  8. (with M. Hull) Random walks and quasi-convexity in acylindrically hyperbolic groups.  arXiv:1909.10876.  J. Topol. 14(3): 992--1026, 2023.
  9. (with J. Behrstock) Conjugator lengths in hierarchically hyperbolic groups.  arXiv:1808.09604. Groups Geom. Dyn. 17(3): 805--838, 2023.
  10. (with A. Rasmussen) Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces.  arXiv:1906.04227​.  Algebra. Geom. Topol., 23(4): 1641--1692, 2023.
  11. (with T. Ng and D. Spriano) Uniform exponential growth in hierarchically hyperbolic groups. arXiv:1909.00439.  To appear in Math. Z.
  12. (with A. Rasmussen) Largest hyperbolic actions and quasi-parabolic actions of groups.  arXiv:1910.14157. To appear in J. Topol. Anal.
  13. (with J. Manning) Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups, arXiv:2105.02333. To appear in Mich. Math. J.
  14. (with S. Balasubramanya and A. Rasmussen) Higher rank confining subsets and hyperbolic actions of solvable groups.  arxiv:2108.08175.  Adv. Math. 424, Paper No. 109045, 47pp, 2023.
  15. (with Behrstock, J. and Russell, J.) Structure invariant properties of the hierarchically hyperbolic boundary.  To appear in J. Topol. Anal. arXiv:2208.07930
  16. ​(with Behrstock, J. and Russell, J.) Relative hyperbolicity, thickness, and the hierarchically hyperbolic boundary. arXiv:2305.16906. To appear in Mich. Math. J.
  17. (with S. Balasubramanya and A. Rasmussen) Valuations, completions, and hyperbolic actions of metabelian groups. arxiv.org/abs/2207.12945.  J. Lon. Math. Soc. (2) 109 (2024) no. 6, Paper No. e12916, 72pp.
  18. (with H. T. Nguyen and A. Rasmussen) Largest hyperbolic actions of 3--manifold groups. arXiv:2305.07425.  ​Bull. Load. Math. Soc.​ 56 (2024), no. 10, 3090--3133.
  19. (with N. Miller and P. Patel) Infinite-type loxodromic isometries of the relative arc graph.  arXiv:2109.06106. Algebr. Geom. Topol., 25-1 (2025), 563--644.
  20. ​(with E. Martinez-Pedroza) "The quasi-isometry invariance of the coset intersection complex." arxiv:2404.16628. To appear in Algebr. Geom. Topol.

Preprints:
  1. (with H. Hoganson, M. Loving, P. Patel, and R. Skipper) A new construction of subgroups big mapping class groups.  arXiv: 2109.05976
  2. ​(with N. Miller and P. Patel) Shift maps are not type-preserving.  arXiv:2212.09156
  3. (with M. Incerti-Medici) Hyperbolic projections and topological invariance of sublinear Morse boundaries.  arXiv:2212.09539​
  4. (with M. Hagen, H. Petyt, and A. Zalloum) Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups. arXiv:2305.097
  5. ​(with A. Genevois and E. Martinez-Pedroza) "Homotopy types of complexes of hyperplanes in quasi-median graphs and applications to right-angled Artin groups." arxiv:2503.08411
  6. (with S. Zbinden) "A non-loxodromic Morse element in a Morse local-to-global group." arxiv:2502.21176
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