Additivity of Heegaard genera under annulus sum

Authors

  • Qi-Long Guo College of Science, China University of Petroleum-Beijing, Beijing, China
  • Qian-Hui Dai College of Science, China University of Petroleum-Beijing, Beijing, China
  • Shu-Xin Wang School of Mathematics, Liaoning Normal University, Dalian, Liaoning, China

DOI:

https://doi.org/10.3842/umzh.v78i7-8.9572

Keywords:

Heegaard genus, Heegaard distance, annulus sum,

Abstract

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 $2\bigl(g(M_1) + g(M_2)\bigr) - 1,$ then $g(M) = g(M_1) + g(M_2).$ As a corollary, we present a sufficient condition for the superadditivity of the tunnel number of knots under connected sum.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 7-8, 2026.

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Published

24.07.2026

Issue

Vol. 78 No. 7-8 (2026)

Section

Research articles