Branched spines and Heegaard genus of 3-manifolds

Yuya Koda

Research output: Contribution to journalArticlepeer-review


We prove that an invariant of closed 3-manifolds, called the block number, which is defined via flow-spines, equals the Heegaard genus, except for S 3 and S 2 × S 1. We also show that the underlying 3-manifold is uniquely determined by a neighborhood of the singularity of a flow-spine. This allows us to encode a closed 3-manifold by a sequence of signed labeled symbols. The behavior of the encoding under the connected sum and a criterion for reducibility are studied.

Original languageEnglish
Pages (from-to)285-299
Number of pages15
JournalManuscripta Mathematica
Issue number3
Publication statusPublished - 2007 Jul

ASJC Scopus subject areas

  • Mathematics(all)


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