Daniel Groves
Research Papers
(see also the ArXiv, which has my more recent papers)

Published Papers

  • A note on nonidentical Lie relators, Journal of Algebra, 211 (1999), 15--25. Abstract.

  • Some properties of free groups of some soluble varieties of groups, J. London Math. Soc. (2) 63 (2001), 592-606. Abstract.

  • Free groups of outer commutator varieties of groups, J. London Math. Soc. (2) 64 (2001), 423-435. Abstract.

  • The Wielandt subalgebra of a Lie algebra (with D. Barnes), J. Aust. Math. Soc. 74 (2003), 313-330. Abstract.

  • Finite groups of bounded exponent (with M.R. Vaughan-Lee), Bull. London Math. Soc. 35 (2003) 37-40. Abstract.

  • Limits of (certain) CAT(0) groups, I: Compactification, Algebraic and Geometric Topology, 5 (2005), 1325-1364. Abstract.

  • Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams, Geometry & Topology, 9 (2005), 2319-2358. Abstract.

  • Fillings, finite generation and direct limits of relatively hyperbolic groups (with J. F. Manning ), Groups, Geometry, and Dynamics, 1 (2007), 329-342. Abstract.

  • The isomorphism problem for toral relatively hyperbolic groups (with F. Dahmani ), Publ. Math. IHES, 107 (2008), 211-290. Abstract.

  • Detecting free splittings in relatively hyperbolic groups (with F. Dahmani ), Transactions of the AMS, 360 (2008), 6303-6318. Abstract. Published here.

  • Dehn filling in relatively hyperbolic groups, (with J.F. Manning ), Israel Journal of Mathematics, 168 (2008), 317-429. Abstract.

  • Residual finiteness, QCERF and fillings of hyperbolic groups (with Ian Agol and Jason Manning), Geometry and Topology, 13 (2009) 1043-1073. Abstract.

  • Enumerating limit groups (with H. Wilton), Groups, Geometry and Dynamics, 3 (2009), 389-399. Abstract.

  • Limit groups for relatively hyperbolic groups, I: The basic tools, Algebraic and Geometric Topology, 9 (2009) 1423-1466. Abstract.

  • Conjugacy classes of solutions to equations and inequations over hyperbolic groups (with H. Wilton), Journal of Topology, 3 (2010), 311--332.Abstract.

  • Cofinitely Hopfian groups, open mappings and knot complements (with M. Bridson, J. Hillman and G. Martin). Groups, Geometry and Dynamics, 4 (2010), 693--707. Abstract.

  • Test elements in torsion-free hyperbolic groups, New York Journal of Mathematics, 18 (2012) 651--656. Abstract. Published here.

  • Appendix to `The Virtual Haken Conjecture' by Ian Agol (with I. Agol and J.F. Manning), Documenta Mathematica, 18 (2013), 1045-1087. Published here.

  • An alternate proof of Wise's Malnormal Special Quotient Theorem (with I. Agol and J.F. Manning.), Forum of Mathematics, Pi 4, e1 (2016) Published here. Abstract.

  • Abelian splittings of right-angled Artin groups (with M. Hull) in Hyperbolic geometry and geometric group theory, Advanced Studies in Pure Mathematics Mathematical Society of Japan, 73 (2017), pp. 159-165.

  • Dehn fillings and elementary splittings (with J.F. Manning.) Transactions of the American Mathematical Society, 370 (2018), 3017-3051. Published here. Abstract.

  • The structure of limit groups over hyperbolic groups (with Henry Wilton) Israel Journal of Mathematics, 226 (2018), 119-176. Abstract.

  • Homomorphisms to acylindrically hyperbolic group I: Equationally noetherian groups (with Michael Hull) Transactions of the American Mathematical Socety, 372 (2019), 7141--7190. Abstract.

  • Immutability is not uniformly decidable in hyperbolic groups (with H. Wilton) In Beyond hyperbolicity, LMS Lecture Note Series 454 (2019), 179-185. Abstract.

  • Boundaries of Dehn fillings (with J.F. Manning and Alessandro Sisto) Geometry and Topology, 23 (2019), 2929-3002. Abstract.

  • Relative Cubulations and groups with a 2-sphere boundary (with E. Einstein) Compositio Mathematica, 156 (2020), 862-867. Abstract.

  • Quasiconvexity and Dehn filling (with J.F. Manning) American Journal of Mathematics, 143, no.1 (2021), 95-124. Abstract.

  • Relatively geometric actions on CAT(0) cube complexes (with E. Einstein) Journal of the London Mathematical Society, 105, no.1 (2022), 691-708. Abstract.

  • Specializing cubulated relatively hyperbolic groups (with J.F. Manning) Journal of Topology, 15, no. 2 (2022), 398-442. Abstract.

  • Prescribed virtual homological torsion of 3-manifolds (with M. Chu) Journal of the Institute of Mathematics of Jussieu, (2022) published online, issue and page numbers to occur later. Abstract

  • Special IMM groups (with J.F. Manning.) Abstract. Bulletin of the London Mathematical Society 55, no.2 (2023), 717-722.

  • Hyperbolic groups acting improperly (with J.F. Manning.) Abstract. Geometry and Topology 27 (2023), 3387-3460.

  • Separation and relative quasi-convexity for relatively geometric actions (with E. Einstein and Thomas Ng). Abstract. Groups, geometry, and dynamics, 18 (2024), 649-676.


    Book

  • The quadratic isoperimetric inequality for mapping tori of free group automorphisms (with Martin Bridson). Memoirs of the AMS, 203 (2010), no. 955. Abstract.

    Note: This monograph contains the contents of the three papers on (mapping tori of) free group automorphisms with Martin Bridson which are listed below. They will not be published separately.


    Preprints



  • Recognizing geometric 3-manifold groups using the word problem (with J.F. Manning and H. Wilton.) .pdf Abstract.

  • Homomorphisms to 3-manifold groups (with M. Hull and H. Liang) .pdf Abstract

  • Relatively geometric actions of Kahler groups on CAT(0) cube complexes (with Corey Bregman and Kejia Zhu). .pdf Abstract. Algebraic and Geometric Topology, to appear.

  • Appendix to 'Relative cubulation of relative strict hyperbolization' by J.F. Lafont and L. Ruffoni (with J.F. Manning). .pdf.

  • Drilling hyperbolic groups (with P. Haïssinsky, J.F. Manning, D. Osajda, A. Sisto, and G. Walsh). .pdf.


    E-Prints

    (Not for publication)

  • The quadratic isoperimetric inequality for mapping tori of free group autmorphisms, I: Positive automorphisms (with Martin Bridson). Preprint (2003). Abstract. .pdf (666k)
    This paper now forms Part I of the above monograph with Bridson, and will not be published separately.


  • Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument. Preprint (2004). Abstract .pdf (336k)
    This paper will not be published since its results are now contained in the revised version of `Limit groups for relatively hyperbolic groups, I' above.


  • Free group automorphisms, train tracks and the beaded decomposition (with Martin Bridson). Preprint (2005). Abstract. .pdf (323k)
    This paper now forms Part II of the above monograph with Bridson and will not be published separately.


  • The quadratic isoperimetric inequality for mapping tori of free group automorphisms, II: The general case (with Martin Bridson). Preprint (2006). Abstract. .pdf (485k)
    This paper now forms Part III of the above monograph with Bridson and will not be published separately.



    • Some of the research above is based upon work supported by the National Science Foundation under Grant Numbers: DMS-0504251, DMS-0813863, DMS-0804365, DMS-0953794 (CAREER), DMS-1507067, DMS-1904913, DMS-2037569 (RTG), and DMS-2203343, and by Simons Fellowships in 2015-16, and 2023-24.

    Any opinions, findings, conclusions or recommendations expresesd in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or the Simons Foundation.