Orderability of big mapping class groups
| Autor: | Kumar, Pravin, Sanghi, Apeksha, Singh, Mahender |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander system for the surface using a carefully chosen exhaustion by finite-type subsurfaces. In fact, we prove that a generalised ideal arc system for the surface also induces a left-ordering on the big mapping class group. We then prove that two generalised ideal arc systems determine the same left-ordering if and only if they are loosely isotopic. Finally, we prove that the topology on the big mapping class group is the same as the order topology induced by a left-ordering corresponding to an inductively constructed ideal arc system. Comment: 22 pages, 19 figures |
| Databáze: | arXiv |
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