Abstract
It is known that each compact connected orientable 3-manifold M with boundary admits an H′-splitting H1 ∪FH2, where F is a compact connected orientable surface properly embedded in M and splits M into two handlbodies H1 and H2. In this paper, we show that a non-completely L-reducible and minimal H′-splitting surface for a compact connected irreducible orientable anannular Seifert 3-manifold with boundary is horizontal, and give a necessary and sufficient condition for an amalgamation of two compact connected orientable 3-manifolds along a compact connected surface to be a Seifert manifold with boundary, and describe a characteristic of some H′-splittings to denote a Seifert 3-manifold with boundary. For a compact connected orientable Seifert manifold M with a semi-bundle structure M1 ∪FM2, we give an upper bound of the genus of the base surface.
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The authors wish to thank the referees for many helpful suggestions.
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Supported in part by (Grant No. 12071051) of NSFC and the Fundamental Research Funds (Grant No. DUT21LAB302) for the Central Universities
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Xu, Y., Lei, F.C. & Li, F.L. H′-splittings of Seifert Manifolds with Boundary. Acta. Math. Sin.-English Ser. 39, 695–706 (2023). https://doi.org/10.1007/s10114-023-2203-x
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DOI: https://doi.org/10.1007/s10114-023-2203-x