Additivity of Heegaard genera of bounded surface sums
| dc.creator | Qiu, Ruifeng | |
| dc.creator | Wang, Shicheng | |
| dc.creator | Zhang, Mingxing | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T09:45:19Z | |
| dc.date.available | 2026-07-07T09:45:19Z | |
| dc.description | Let $M$ be a surface sum of 3-manifolds $M_1$ and $M_2$ along a bounded connected surface $F$ and $\partial_i$ be the component of $\partial M_i$ containing $F$. If $M_i$ has a high distance Heegaard splitting, then any minimal Heegaard splitting of $M$ is the amalgamation of those of $M^1, M^2$ and $M^*$, where $M^i=M_i\setminus\partial_i\times I$, and $M^{*}=\partial_1\times I\cup_{F} \partial_2\times I$. Furthermore, once both $\partial_i\setminus F$ are connected, then $g(M) = Min\bigl\{g(M_1)+g(M_2), α\bigr\}$, where $α= g(M_1) + g(M_2) + 1/2(2χ(F) + 2 - χ(\partial_1) - χ(\partial_2)) - Max\bigl\{g(\partial_1), g(\partial_2)\bigl\}$; in particular $g(M)=g(M_1)+g(M_2)$ if and only if $χ(F)\geq 1/2Max\bigl\{χ(\partial_1), χ(\partial_2)\bigr\}.$ The proofs rely on Scharlemann-Tomova's theorem. | |
| dc.identifier | https://arxiv.org/abs/0806.2934 | |
| dc.identifier | http://arxiv.org/abs/0806.2934 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163155 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | Additivity of Heegaard genera of bounded surface sums | |
| dc.type | text |