AI 中文总结
研究当n≥4时n股辫群Bₙ是否剩余有限刚性，通过展示一族特殊有限生成剩余有限群与Bₙ有相同剩余有限完备化来证明其非剩余有限刚性，给出非剩余有限刚性映射类群首个例子。
AI 中文摘要
我们证明当n≥4时，n股辫群Bₙ不是剩余有限刚性的。通过展示一族两两不同构、有限生成的剩余有限群，它们与Bₙ有相同的剩余有限完备化来证明。这否定地回答了一个著名问题，并给出了非剩余有限刚性映射类群的首个已知例子。
英文摘要
We show that the $n$-strand braid group $\mathbf{B}_n$ is not profinitely rigid when $n \geq 4$. We do this by exhibiting a family of pairwise non-isomorphic, finitely presented residually finite groups with the same profinite completion as $\mathbf{B}_n$. This answers a well-known problem negatively, and gives the first known examples of non-profinitely rigid mapping class groups.
Comments4 pages. Comments welcome!
