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Surface complexes of Seifert fibered spaces


Author: Jennifer Schultens
Journal: Proc. Amer. Math. Soc. 148 (2020), 3633-3645
MSC (2010): Primary 57M50
DOI: https://doi.org/10.1090/proc/15081
Published electronically: May 11, 2020
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Abstract: We define the surface complex for $ 3$-manifolds and embark on a case study in the arena of Seifert fibered spaces. The base orbifold of a Seifert fibered space captures some of the topology of the Seifert fibered space, so, not surprisingly, the surface complex of a Seifert fibered space always contains a subcomplex isomorphic to the curve complex of the base orbifold. How this subcomplex sits inside the surface complex depends on the Seifert invariants.


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Jennifer Schultens
Affiliation: Department of Mathematics, University of California, Davis, Davis, 1 Shields Avenue, California 95616

DOI: https://doi.org/10.1090/proc/15081
Received by editor(s): April 1, 2019
Received by editor(s) in revised form: July 12, 2019, August 29, 2019, and September 4, 2019
Published electronically: May 11, 2020
Communicated by: Davis Futer
Article copyright: © Copyright 2020 American Mathematical Society