High distance Heegaard splittings from involutions

Fixed an oriented handlebody H = H + with boundary F, let η ( H + ) = H − be the mirror image of H + along F, so η ( F ) is the boundary of H − , for a map f : F → F , we have a 3-manifold by gluing H + and H − along F with attaching map f, and denote it by M f = H + ∪ f : F → F H − . In this note,...

Full description

Saved in:
Bibliographic Details
Published inTopology and its applications Vol. 158; no. 3; pp. 409 - 411
Main Author Ma, Jiming
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.02.2011
Subjects
Heegaard distance
Mapping class group
Heegaard distance
57M
Mapping class group
Online AccessGet full text

Cover

More Information
Summary:Fixed an oriented handlebody H = H + with boundary F, let η ( H + ) = H − be the mirror image of H + along F, so η ( F ) is the boundary of H − , for a map f : F → F , we have a 3-manifold by gluing H + and H − along F with attaching map f, and denote it by M f = H + ∪ f : F → F H − . In this note, we show that there are involutions f : F → F which are also reducible, such that M f have arbitrarily high Heegaard distances.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2010.11.016