Additivity of Heegaard genera under annulus sum

• Date: 2026
• Main Authors: Guo, Qi-Long, Dai, Qian-Hui, Wang, Shu-Xin
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9572
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 515.162 Let $M$ be a compact 3-manifold containing an essential annulus $A$  separating $M$ into two manifolds $M_1$ and $M_2.$ We prove that if, for each $i=1,2,$ $g(M_i) \geq 2$  and $M_i$ admits a Heegaard splitting with Heegaard distance not smaller than $2\bigl(g(M_1) + g(M_2)\bigr) - 1,$ t...