Open Access
June 2006 On DS-diagrams for 3-manifolds of Heegaard Genus 2
Mariko Endoh
Tokyo J. Math. 29(1): 117-146 (June 2006). DOI: 10.3836/tjm/1166661871


The block number $Bl(M)$ introduced in our previous paper is a new topological invariant of a closed orientable 3-manifold $M$ which estimates a combinatorial complexity of $M$ just like the Heegaard genus $HG(M)$. In our previous paper, we have shown an inequality $HG(M) \leq Bl(M)$ for any $M \ne S^2 \times S^1$. In this paper, we will show that $Bl(M)=HG(M)$ for any $M$ with $HG(M)=2$ and moreover that $Bl(M) \leq 4$ for any $M$ with $HG(M)=3$.


Download Citation

Mariko Endoh. "On DS-diagrams for 3-manifolds of Heegaard Genus 2." Tokyo J. Math. 29 (1) 117 - 146, June 2006.


Published: June 2006
First available in Project Euclid: 20 December 2006

zbMATH: 1111.57015
MathSciNet: MR2258276
Digital Object Identifier: 10.3836/tjm/1166661871

Rights: Copyright © 2006 Publication Committee for the Tokyo Journal of Mathematics

Vol.29 • No. 1 • June 2006
Back to Top