Surfaces, circles, and solenoids

Details Surfaces, circles, and solenoids Surfaces, circles, and solenoids

2004-09-17

arxiv.org/abs/math/0409309v1

Mathematics

Geometric Topology

18 pages, 2 figures

Scientific paper

Previous work of the author has developed coordinates on bundles over the classical Teichmueller spaces of punctured surfaces and on the space of cosets of the Moebius group in the group of orientation-preserving homeomorphisms of the circle, and this work is surveyed here. Joint work with Dragomir Saric is also sketched which extends these results to the setting of the Teichmueller space of the solenoid of a punctured surface, which is defined here in analogy to Dennis Sullivan's original definition for the case of closed surfaces. Because of relations with the classical modular group, the punctured solenoid and its Teichmueller theory have connections with number theory.

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