Haken spheres for genus two Heegaard splittings

Sangbum Cho, Yuya Koda

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A manifold which admits a reducible genus-2 Heegaard splitting is one of the 3-sphere, S2 × S1, lens spaces or their connected sums. For each of those splittings, the complex of Haken spheres is defined. When the manifold is the 3-sphere, S2 × S1 or a connected sum whose summands are lens spaces or S2 × S1, the combinatorial structure of the complex has been studied by several authors. In particular, it was shown that those complexes are all contractible. In this work, we study the remaining cases, that is, when the manifolds are lens spaces. We give a precise description of each of the complexes for the genus-2 Heegaard splittings of lens spaces. A remarkable fact is that the complexes for most lens spaces are not contractible and even not connected.

Original languageEnglish
Pages (from-to)563-572
Number of pages10
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume165
Issue number3
DOIs
StatePublished - 2018 Nov 1

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