Mapping class group of a handlebody

Volume 158 / 1998

Bronisław Wajnryb Fundamenta Mathematicae 158 (1998), 195-228 DOI: 10.4064/fm-158-3-195-228


Let B be a 3-dimensional handlebody of genus g. Let ℳ be the group of the isotopy classes of orientation preserving homeomorphisms of B. We construct a 2-dimensional simplicial complex X, connected and simply-connected, on which ℳ acts by simplicial transformations and has only a finite number of orbits. From this action we derive an explicit finite presentation of ℳ.


  • Bronisław Wajnryb

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