We provide a pure algebraic version of the first-named author’s dynamical characterization of the Conrad property for group orderings. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof of a theorem first established by Linnell: an orderable group having infinitely many orderings has uncountably many. This proof is achieved by extending to uncountable orderable groups a result about orderings which may be approximated by their conjugates. This last result is illustrated by an example of an exotic ordering on the free group given by the third author in the Appendix.
Navas, Andrés 1 ; Rivas, Cristóbal 2
@article{10_2140_agt_2009_9_2079,
author = {Navas, Andr\'es and Rivas, Crist\'obal},
title = {A new characterization of {Conrad{\textquoteright}s} property for group orderings, with applications},
journal = {Algebraic and Geometric Topology},
pages = {2079--2100},
year = {2009},
volume = {9},
number = {4},
doi = {10.2140/agt.2009.9.2079},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.2079/}
}
TY - JOUR AU - Navas, Andrés AU - Rivas, Cristóbal TI - A new characterization of Conrad’s property for group orderings, with applications JO - Algebraic and Geometric Topology PY - 2009 SP - 2079 EP - 2100 VL - 9 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.2079/ DO - 10.2140/agt.2009.9.2079 ID - 10_2140_agt_2009_9_2079 ER -
%0 Journal Article %A Navas, Andrés %A Rivas, Cristóbal %T A new characterization of Conrad’s property for group orderings, with applications %J Algebraic and Geometric Topology %D 2009 %P 2079-2100 %V 9 %N 4 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.2079/ %R 10.2140/agt.2009.9.2079 %F 10_2140_agt_2009_9_2079
Navas, Andrés; Rivas, Cristóbal. A new characterization of Conrad’s property for group orderings, with applications. Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 2079-2100. doi: 10.2140/agt.2009.9.2079
[1] , , Orderable groups, 27, Marcel Dekker (1977)
[2] , Isolated points in the space of left orderings of a group, preprint (2008)
[3] , Right-ordered groups, Michigan Math. J. 6 (1959) 267
[4] , , The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group, Invent. Math. 145 (2001) 19
[5] , Braid groups and left distributive operations, Trans. Amer. Math. Soc. 345 (1994) 115
[6] , , , , Why are braids orderable?, 14, Société Mathématique de France (2002)
[7] , , On braid groups, Mat. Sb. 192 (2001) 53
[8] , , Right-ordered groups, , Consultants Bureau (1996)
[9] , Noncommutative localization in group rings, from: "Non-commutative localization in algebra and topology", London Math. Soc. Lecture Note Ser. 330, Cambridge Univ. Press (2006) 40
[10] , An even better representation for free lattice-ordered groups, Trans. Amer. Math. Soc. 290 (1985) 81
[11] , Amenable groups that act on the line, Algebr. Geom. Topol. 6 (2006) 2509
[12] , Grupos de difeomorfismos del círculo, 13, Sociedade Brasileira de Matemática (2007)
[13] , On the dynamics of left-orderable groups, preprint (2007)
[14] , Topology on the spaces of orderings of groups, Bull. London Math. Soc. 36 (2004) 519
[15] , On groups with an infinite set of right orders, Sibirsk. Mat. Zh. 38 (1997) 90
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