Path-connectivity of the set of uniquely ergodic and cobounded foliations
Jon Chaika, Sebastian Hensel
TL;DR
This paper proves that for certain surfaces, the sets of uniquely ergodic and cobounded foliations are both path-connected and locally path-connected, enhancing understanding of their topological structure.
Contribution
It establishes the path-connectedness and local path-connectedness of these foliation sets for surfaces of genus at least 2 with marked points or genus at least 5.
Findings
Sets are path-connected for specified surfaces
Sets are locally path-connected for specified surfaces
Advances understanding of foliation topology
Abstract
We show that for a closed surface of genus at least 5, or a surface of genus at least 2 with at least one marked point, the set of uniquely ergodic foliations and the set of cobounded foliations is path-connected and locally path-connected.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Stochastic processes and statistical mechanics