Algebraic & Geometric Topology Volume 26, issue 4 (2026)

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ISSN (electronic): 1472-2739

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Finiteness properties of some groups of piecewise projective homeomorphisms

Daniel S. Farley

Algebraic & Geometric Topology 26 (2026) 1395–1449

DOI: 10.2140/agt.2026.26.1395

Bibliography

1	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
2	A Björner, Topological methods, from: "Handbook of combinatorics, II" (editors R L Graham, M Grötschel, L Lovász), Elsevier Sci. B. V. (1995) 1819 MR1373690
3	K S Brown, Finiteness properties of groups, J. Pure Appl. Algebra 44 (1987) 45 MR885095
4	A Buss, R Exel, R Meyer, Inverse semigroup actions as groupoid actions, Semigroup Forum 85 (2012) 227 MR2969047
5	J W Cannon, W J Floyd, W R Parry, Introductory notes on Richard Thompson’s groups, Enseign. Math. (2) 42 (1996) 215 MR1426438
6	D S Farley, B Hughes, Finiteness properties of locally defined groups, (2020) arXiv:2010.08035
7	J M Howie, An introduction to semigroup theory, 7, Academic (1976) MR466355
8	Y Lodha, A nonamenable type F_∞ group of piecewise projective homeomorphisms, J. Topol. 13 (2020) 1767 MR4186144
9	Y Lodha, J T Moore, A nonamenable finitely presented group of piecewise projective homeomorphisms, Groups Geom. Dyn. 10 (2016) 177 MR3460335
10	Y Lodha, M C B Zaremsky, The BNSR-invariants of the Lodha–Moore groups, and an exotic simple group of type F_∞, Math. Proc. Cambridge Philos. Soc. 174 (2023) 25 MR4523108
11	N Monod, Groups of piecewise projective homeomorphisms, Proc. Natl. Acad. Sci. USA 110 (2013) 4524 MR3047655
12	M H A Newman, On theories with a combinatorial definition of “equivalence”, Ann. of Math. (2) 43 (1942) 223 MR7372
13	A Y Olshanskii, M V Sapir, Non-amenable finitely presented torsion-by-cyclic groups, Publ. Math. Inst. Hautes Études Sci. 96 (2002) 43 MR1985031
14	J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (2006) MR2249478
15	M Stein, Groups of piecewise linear homeomorphisms, Trans. Amer. Math. Soc. 332 (1992) 477 MR1094555