For a bridge decomposition of a link in the $3$-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the $3$-sphere that preserve each of the bridge sphere and link setwise. After describing basic properties of this group, we discuss the asymptotic behavior of the minimal pseudo-Anosov entropies. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings of the $3$-sphere and the real projective space.

中文翻译：

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桥分解的 Goeritz 群

对于$3$-sphere 中链接的桥分解，我们将Goeritz 群定义为$3$-sphere 的保持方向的同胚同胚的同位素类群，它们按组保留桥球和链接中的每一个。在描述了这个群的基本性质之后，我们讨论了最小伪阿诺索夫熵的渐近行为。然后，我们对$3$-球体的 Heegaard 分裂的原始 Goeritz 群和实射影空间的最小熵的渐近行为进行了应用。