Geometry & Topology Volume 30, issue 6 (2026)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Group rings and hyperbolic geometry

Grigori Avramidi and Thomas Delzant

Geometry & Topology 30 (2026) 2337–2365

DOI: 10.2140/gt.2026.30.2337

Bibliography

1	P Abramenko, On finite and elementary generation of SL₂(R), preprint (2008) arXiv:0808.1095
2	G N Arzhantseva, A dichotomy for finitely generated subgroups of word hyperbolic groups, from: "Topological and asymptotic aspects of group theory" (editors R Grigorchuk, M Mihalik, M Sapir, Z Šunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 1 MR2216702
3	G Avramidi, Division in group rings of surface groups, J. Lond. Math. Soc. 106 (2022) 982 MR4477209
4	D Bachman, D Cooper, M E White, Large embedded balls and Heegaard genus in negative curvature, Algebr. Geom. Topol. 4 (2004) 31 MR2031911
5	H Bass, Projective modules over free groups are free, J. Algebra 1 (1964) 367 MR178032
6	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
7	K S Brown, Cohomology of groups, 87, Springer (1994) MR1324339
8	D E Cohen, R C Lyndon, Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963) 526 MR170930
9	P M Cohn, Free ideal rings, J. Algebra 1 (1964) 47 MR161891
10	P M Cohn, On the structure of the GL₂ of a ring, Inst. Hautes Études Sci. Publ. Math. 30 (1966) 5 MR207856
11	P M Cohn, Free ideal rings and free products of rings, from: "Actes du Congrès International des Mathématiciens" (editors M Berger, J Dieudonné, J Leray, J L Lions, P Malliavin, J P Serre), Gauthier-Villars (1971) 273 MR506389
12	P M Cohn, Free ideal rings and localization in general rings, 3, Cambridge Univ. Press (2006) MR2246388
13	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes : les groupes hyperboliques de Gromov, 1441, Springer (1990) MR1075994
14	T Delzant, Sur l’anneau d’un groupe hyperbolique, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 381 MR1440952
15	W Dicks, M J Dunwoody, Groups acting on graphs, 17, Cambridge Univ. Press (1989) MR1001965
16	S Eilenberg, T Ganea, On the Lusternik–Schnirelmann category of abstract groups, Ann. of Math. 65 (1957) 517 MR85510
17	R H Fox, Free differential calculus, I : Derivation in the free group ring, Ann. of Math. 57 (1953) 547 MR53938
18	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
19	M Gromov, Singularities, expanders and topology of maps, I : Homology versus volume in the spaces of cycles, Geom. Funct. Anal. 19 (2009) 743 MR2563769
20	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
21	C Hog-Angeloni, A short topological proof of Cohn’s theorem, from: "Topology and combinatorial group theory" (editor P Latiolais), Lecture Notes in Math. 1440, Springer (1990) 90 MR1082984
22	I Kaplansky, Problems in the theory of rings, from: "Report of a conference on linear algebras" (editor I Kaplansky), National Academy of Sciences–National Research Council 502, Nat. Acad. Sci. (1957) 1 MR96696
23	I Kapovich, R Weidmann, Nielsen methods and groups acting on hyperbolic spaces, Geom. Dedicata 98 (2003) 95 MR1988426
24	S Krstić, J McCool, Free quotients of SL₂(R[x]), Proc. Amer. Math. Soc. 125 (1997) 1585 MR1376995
25	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR163331
26	R Sandling, Graham Higman’s thesis “Units in group rings”, from: "Integral representations and applications" (editor K W Roggenkamp), Lecture Notes in Math. 882, Springer (1981) 93 MR646094
27	J R Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968) 312 MR228573
28	R Thom, Sur une partition en cellules associée à une fonction sur une variété, C. R. Acad. Sci. Paris 228 (1949) 973 MR29160
29	C T C Wall, Finiteness conditions for CW-complexes, Ann. of Math. 81 (1965) 56 MR171284