Non-Left-Orderable 3-Manifold Groups
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 32-40
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We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of ${{S}^{3}}$ branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of ${{S}^{3}}$ branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the ${{5}_{2}}$ knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.
Dąbkowski, Mieczysław K.; Przytycki, Józef H.; Togha, Amir A. Non-Left-Orderable 3-Manifold Groups. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 32-40. doi: 10.4153/CMB-2005-003-6
@article{10_4153_CMB_2005_003_6,
author = {D\k{a}bkowski, Mieczys{\l}aw K. and Przytycki, J\'ozef H. and Togha, Amir A.},
title = {Non-Left-Orderable {3-Manifold} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {32--40},
year = {2005},
volume = {48},
number = {1},
doi = {10.4153/CMB-2005-003-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-003-6/}
}
TY - JOUR AU - Dąbkowski, Mieczysław K. AU - Przytycki, Józef H. AU - Togha, Amir A. TI - Non-Left-Orderable 3-Manifold Groups JO - Canadian mathematical bulletin PY - 2005 SP - 32 EP - 40 VL - 48 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-003-6/ DO - 10.4153/CMB-2005-003-6 ID - 10_4153_CMB_2005_003_6 ER -
%0 Journal Article %A Dąbkowski, Mieczysław K. %A Przytycki, Józef H. %A Togha, Amir A. %T Non-Left-Orderable 3-Manifold Groups %J Canadian mathematical bulletin %D 2005 %P 32-40 %V 48 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-003-6/ %R 10.4153/CMB-2005-003-6 %F 10_4153_CMB_2005_003_6
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