We show that for every integer \(b\ge 3\) and every integer k with \(1\le k\le b\), there exists an alternating k-component link in a b-bridge position with respect to a critical bridge sphere. In fact, for each b, we construct an infinite family of links whose bridge spheres are critical.

中文翻译：

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关键桥梁球体，用于与任意多个桥梁的链接

我们表明，对于每个整数\（b \ ge 3 \）和每个具有\（1 \ le k \ le b \）的整数k，相对于临界点，它在b桥位置处存在交替的k分量链接桥梁领域。实际上，对于每个b，我们构造了一个无限的连接族，其桥球至关重要。