The topology on the space of left orderings of a group

Details The topology on the space of left orderings of a group The topology on the space of left orderings of a group

2006-07-19

arxiv.org/abs/math/0607470v2

Mathematics

Group Theory

This paper has been withdrawn. Adam S. Sikora has pointed out that the proof of Lemma 2.3 is wrong. It is not clear if the Lem

Scientific paper

Let G be a group and let O_G denote the set of left orderings on G. Then O_G can be topologized in a natural way, and we shall study this topology to answer three conjectures. In particular we shall show that O_G can never be countably infinite. Furthermore in the case G is a countable nonabelian free group, we shall show that O_G is homeomorphic to the Cantor set and that the positive cone of a left order on G is not finitely generated. Generalizations to locally indicable groups will also be considered.

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