可加隧道数与本原元
Additive tunnel number and primitive elements
摘要：
本文证明了：如果3-球面中两个1号隧道纽结的连通和是2号隧道纽结，则至少有一个被加数纽结具有亏格2 Heegaard分裂，其中子午线作为本原元.因此，这是隧道1号节点具有附加隧道数的充要条件。
英文摘要：
It is proven here that if the connected sum of two tunnel number one knots in the 3-sphere is a tunnel number two knot, then at least one of the summand knots has a genus two Heegaard splitting with a meridian as a primitive element. Hence this is a necessary and sufficient condition for tunnel number one knots to have additive tunnel number.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
