The complex of essential surfaces is contractible

The complex of essential surfaces is contractible

Let M be a 3-manifold and S be a component of ∂M. We introduce a simplicial complex E(M,S), whose vertices are isotopy classes of compact essential surfaces in M with at least one boundary component lying on S. E(M,S) can be thought as an analogy to the arc complex of a surface. We show that if M is...

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Veröffentlicht in:Topology and its applications 2022-01, Vol.305, p.107903, Article 107903
Hauptverfasser: Zhang, Faze, Guo, Qilong
Format: Artikel
Sprache:eng
Schlagworte:
Contractible
Essential surface
Simplicial complex
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Zusammenfassung:Let M be a 3-manifold and S be a component of ∂M. We introduce a simplicial complex E(M,S), whose vertices are isotopy classes of compact essential surfaces in M with at least one boundary component lying on S. E(M,S) can be thought as an analogy to the arc complex of a surface. We show that if M is irreducible and S is compressible in M, then E(M,S) is contractible.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2021.107903