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A step towards twist conjecture. (English) Zbl 07009278
Summary: Under the assumption that a defining graph of a Coxeter group admits only twists in \(\mathbb{Z}_2\) and is of type FC, we prove Mühlherr’s Twist Conjecture.
MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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[1] Noel Brady, Jonathan P. McCammond, Bernhard M\"uhlherr, and Walter D. Neumann. Rigidity of Coxeter groups and Artin groups. Geometriae Dedicata, 94(1):91–109, 2002. DOI 10.1023/A:1020948811381; zbl 1031.20035; MR1950875 · Zbl 1031.20035
[2] Pierre-Emmanuel Caprace and Bernhard M\"uhlherr. Reflection rigidity of 2-spherical Coxeter groups. Proceedings of the London Mathematical Society, 94(2):520–542, 2007. DOI 10.1112/plms/pdl015; zbl 1140.20032; MR2311001 · Zbl 1140.20032
[3] Pierre-Emmanuel Caprace and Piotr Przytycki. Twist-rigid Coxeter groups. Geometry & Topology, 14(4):2243–2275, 2010. DOI 10.2140/gt.2010.14.2243; zbl 1210.20037; MR2740646; arxiv 0911.0354 · Zbl 1210.20037
[4] Ruth Charney and Michael Davis. When is a Coxeter system determined by its Coxeter group? J. London Math. Soc. (2), 61(2):441–461, 2000. DOI 10.1112/S0024610799008583; zbl 0983.20034; MR1760693 · Zbl 0983.20034
[5] Jean-Yves H\'ee. Le c\^one imaginaire d’une base de racines sur R. Th\`ese d’\'etat, Universit\'e d’Orsay, 1990
[6] Robert B. Howlett, Peter J. Rowley, and Donald E. Taylor. On outer automorphism groups of Coxeter groups. Manuscripta Math., 93(4):499–513, 1997. DOI 10.1007/BF02677488; zbl 0888.20023; MR1465894 · Zbl 0888.20023
[7] Robert B. Howlett and Bernhard M\"uhlherr. Isomorphisms of Coxeter groups which do not preserve reflections. preprint, 2004
[8] Michael R. Laurence. A generating set for the automorphism group of a graph group. Journal of the London Mathematical Society, 52(2):318–334, 1995. DOI 10.1112/jlms/52.2.318, zbl 0836.20036; MR1356145 · Zbl 0836.20036
[9] Timoth\'ee Marquis and Bernhard M\"uhlherr. Angle-deformations in Coxeter groups. Algebr. Geom. Topol., 8(4):2175–2208, 2008. DOI 10.2140/agt.2008.8.2175; zbl 1184.20032; MR2465738; arxiv 0810.3392 · Zbl 1184.20032
[10] Bernhard M\"uhlherr. Automorphisms of graph-universal Coxeter groups. \em Journal of Algebra, 200(2):629–649, 1998. DOI 10.1006/jabr.1997.7230; zbl 0897.20033; MR1610676 · Zbl 0897.20033
[11] Bernhard M\"uhlherr. The isomorphism problem for Coxeter groups. In The Coxeter legacy, pages 1–15. Amer. Math. Soc., Providence, RI, 2006. zbl 1103.20031; MR2209018 · Zbl 1103.20031
[12] Bernhard M\"uhlherr and Richard Weidmann. Rigidity of skew-angled Coxeter groups. Adv. Geom, 2(4):391–415, 2002. DOI 10.1515/advg.2002.018; zbl 1015.20029; MR1941338 · Zbl 1015.20029
[13] John G. Ratcliffe and Steven T. Tschantz. Chordal Coxeter groups. Geom. Dedicata, 136:57–77, 2008. DOI 10.1007/s10711-008-9274-9; zbl 1175.20031; MR2443343; arxiv math/0607301 · Zbl 1175.20031
[14] Mark Ronan. Lectures on Buildings: Updated and Revised. University of Chicago Press, 2009. zbl 1190.51008; MR2560094 · Zbl 1190.51008
[15] Christian Weigel. The twist conjecture for Coxeter groups without small triangle subgroups. Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial, 12(1):111–140, 2011. zbl 1284.20042; MR2942720 · Zbl 1284.20042
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