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Showing 1 to 5 of 5 for “"left-orderable"”.
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Left Orderable Residually Finite p-groups
… q-group. We conjecture that such groups G are left orderable. In this paper we show some results which came as attempts to prove this conjecture. In particular we give a condition under which split extensions of residually finite p-groups are again residually finite p-groups. We also give an …
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New Methods for Finding Non-Left-Orderable and Unique Product Groups
… present techniques for proving a group to be non-left-orderable or a unique product group. These methods involve the existence of a mapping from the group to R which obeys a left-multiplication criterion. By determining the existence or non-existence of such a mapping, the desired information …
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Left-orderability of Dehn surgeries on knot complements
… criterion for the existence of an interval of left orderable Dehn surgeries on M. We apply this criterion to prove that the two-bridge knot that corresponds to the continued fraction [1,1,2,2,2j] for j >= 1 and the (-3,3,2j+1)-pretzel knot admit an interval of left orderable Dehn surgeries. …
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Orderability of homology spheres obtained by Dehn filling
In my thesis, I study left-orderability of $\mathbb{Q}$-homology spheres. I use $\widetilde{PSL_2\mathbb{R}}$ representations as a tool. First, I showed this tool has its limitations by constricting a series of $\mathbb{Z}$-homology spheres with potentially left-orderable fundamental groups but no …
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The Space of Left Orders on a Group
The study of orderable groups is a topic that is all too often overlooked as a topic in algebra. The subject of orderable groups is a field of study which is directly associated with algebraic group theory, algebraic topology, and set theory. This paper will act as a guide into the world of …