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Creators/Authors contains: "Al_Beaini, Alina"

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  1. ; ; (, Groups, Geometry, and Dynamics)
    For each circle bundleS^{1}\to X\to\Sigma_{g}over a surface with genusg\ge2, there is a natural surjection\pi:\operatorname{Homeo}^{+}(X)\to\operatorname{Mod}(\Sigma_{g}). WhenXis the unit tangent bundleU\Sigma_{g}, it is well known that\pisplits. On the other hand,\pidoes not split when the Euler numbere(X)is not divisible by the Euler characteristic\chi(\Sigma_{g})by Chen and Tshishiku (2023). In this paper, we show that this homomorphism does not split in many cases where\chi(\Sigma_{g})dividese(X). 
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    Free, publicly-accessible full text available May 29, 2026