Abstract
Based on the action of the mapping class group on the space of measured foliations, we construct a new boundary of the mapping class group and study the structure of this boundary. As an application, for any point in Teichmüller space, we consider the orbit of this point under the action of the mapping class group and describe the closure of this orbit in the Thurston compactification and the Gardiner–Masur compactification of Teichmüller space. We also construct some new points in the Gardiner–Masur boundary of Teichmüller space.
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Acknowledgements
The authors would like to thank the referee(s) for the careful reading and many valuable suggestions, especially for informing the new boundary constructed by Hamenstädt [7].
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Supported by NSFC (Grant No. 11771456)
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Liu, L.X., Shi, Y.Z. A New Boundary of the Mapping Class Group. Acta. Math. Sin.-English Ser. 39, 885–903 (2023). https://doi.org/10.1007/s10114-023-1503-5
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DOI: https://doi.org/10.1007/s10114-023-1503-5