Surface complexes of Seifert fibered spaces

Schultens, Jennifer

doi:10.1090/proc/15081

Surface complexes of Seifert fibered spaces
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by Jennifer Schultens PDF

Proc. Amer. Math. Soc. 148 (2020), 3633-3645 Request permission

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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