Among the knots that are the connected sum of two torus knots with cobordism distance 1, we characterise those that have 4-dimensional clasp number at least 2, and we show that their n-fold connected self-sum has 4-dimensional clasp number at least 2n. Our proof works in the topological category. To contrast this, we build a family of topologically slice knots for which the n-fold connected self-sum has 4-ball genus n and 4-dimensional clasp number at least 2n.

中文翻译：

---

关于四维扣结节数的注解

在作为两个环面结的连接和的节点中，cobordism 距离为 1，我们描述了那些具有 4 维扣数至少为 2 的节点，并且我们证明了它们的n重连接自和具有 4 维扣数至少 2 n。我们的证明适用于拓扑范畴。为了对比这一点，我们构建了一系列拓扑切片结，其中n重连接的自和具有 4 球属n和 4 维扣环数至少为 2 n。