TY - JOUR
T1 - Branched spines and Heegaard genus of 3-manifolds
AU - Koda, Yuya
PY - 2007/7
Y1 - 2007/7
N2 - 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.
AB - 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.
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U2 - 10.1007/s00229-007-0097-z
DO - 10.1007/s00229-007-0097-z
M3 - Article
AN - SCOPUS:34547295086
SN - 0025-2611
VL - 123
SP - 285
EP - 299
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 3
ER -