The realization and classification of topologically transitive group actions on $1$-manifolds

Enhui Shi

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arXiv · 1910.11728

The realization and classification of topologically transitive group actions on $1$-manifolds

Enhui Shi

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Abstract

In this report, we first recall the Poincar\'e's classification theorem for minimal orientation-preserving homeomorphisms on the circle and the Ghys' classification theorem for minimal orientation-preserving group actions on the circle. Then we introduce a classification theorem for a specified class of topologically transitive orientation-preserving group actions on the circle by $\mathbb Z^d$. Also, some groups that admit/admit no topologically transitive actions on the line are determined.

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Enhui Shi. 2019-10-25. The realization and classification of topologically transitive group actions on $1$-manifolds. https://arxiv.org/abs/1910.11728

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