Ubiquity of geometric finiteness in mapping class groups of Haken 3-manifolds

Sungbok Hong, Darryl McCullough

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

For a Haken 3-manifold M with incompressible boundary, we prove that the mapping class group H(M) acts properly discontinuously on a contractible simplicial complex, with compact quotient. This implies that every torsionfree subgroup of finite index in H(M) is geometrically finite. Also, a simplified proof of the fact that torsionfree subgroups of finite index in H(M) exist is given. All results are given for mapping class groups that preserve a boundary pattern in the sense of K. Johannson. As an application, we show that if F is a nonempty compact 2-manifold in ∂M such that ∂M - F is incompressible, then the classifying space BDiff(M rel F) of the diffeomorphism group of M relative to F has the homotopy type of a finite aspherical complex.

Original languageEnglish
Pages (from-to)275-301
Number of pages27
JournalPacific Journal of Mathematics
Volume188
Issue number2
Publication statusPublished - 1999 Apr 1

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Mapping Class Group
Finiteness
Subgroup
Diffeomorphism Group
Classifying Space
Homotopy Type
Simplicial Complex
Quotient
Imply

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Ubiquity of geometric finiteness in mapping class groups of Haken 3-manifolds. / Hong, Sungbok; McCullough, Darryl.

In: Pacific Journal of Mathematics, Vol. 188, No. 2, 01.04.1999, p. 275-301.

Research output: Contribution to journalArticle

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