Birman-Hilden property of covering spaces for nonorientable surfaces. (English) Zbl 1458.57020
Ukr. Math. J. 72, No. 3, 348-357 (2020) and Ukr. Mat. Zh. 72, No. 3, 307-315 (2020).
Given a finite branched covering space \(p:\tilde{N}\to N\) between nonorientable surfaces, with \(\tilde{N}\) having negative Euler characteristic, the authors study conditions under which this covering has the Birman-Hilden property. They obtain in this setting of nonorientable surfaces analogues of properties known in the orientable case. In particular, they prove that if \(p\) is fully ramified then it has the Birman-Hilden property, and that if the covering space does not have the Birman-Hilden property, then the covering space obtained
by blowing up the given covering spaces also does not have this property. There are potential applications in the study of mapping class groups.
Reviewer: Athanase Papadopoulos (Strasbourg)
MSC:
| 57M10 | Covering spaces and low-dimensional topology |
| 57M12 | Low-dimensional topology of special (e.g., branched) coverings |
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