Amir Togha | Bronx Community College (original) (raw)
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Papers by Amir Togha
Annals of Pure and Applied Logic, 2010
We investigate computability theoretic and topological properties of spaces of orders on computab... more We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends Sikora's investigation of orders on groups in topology [28] and Solomon's investigation of these orders in computable algebra . Furthermore, we establish that a computable free group F n of rank n > 1 has a bi-order in every Turing degree.
We show that several torsion free 3-manifold groups are not left-orderable. Our examples are grou... more We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers 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
Annals of Pure and Applied Logic, 2010
We investigate computability theoretic and topological properties of spaces of orders on computab... more We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends Sikora's investigation of orders on groups in topology [28] and Solomon's investigation of these orders in computable algebra . Furthermore, we establish that a computable free group F n of rank n > 1 has a bi-order in every Turing degree.
We show that several torsion free 3-manifold groups are not left-orderable. Our examples are grou... more We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers 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