Profinite刚性性与quandle着色
Profinite rigidity and quandle colourings
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中文总结 AI 辅助
本文证明链环的有限quandle着色数等价于其外围系统的profinite完备化，将经典完备性问题转化为profinite刚性性，并发展了profinite quandle理论。
中文摘要 AI 辅助
我们证明了链环被所有有限quandle着色的数量，作为链环的不变量，等价于外围系统的profinite完备化。这使我们能够将前者不变量的完备性这一经典问题重新表述为profinite刚性性问题。我们还发展了一些profinite quandle理论，并证明了一个拓扑quandle是profinite的当且仅当它是紧致且完全不连通的，并且其内自同构群在其同胚群中是相对紧致的。
英文摘要
We show that the numbers of colourings of a link by all finite quandles is equivalent, as an invariant of links, to the profinite completion of the peripheral system. This allows us to reformulate the classical question of the completeness of the former invariant in terms of profinite rigidity. We also develop some profinite quandle theory, and we show that a topological quandle is profinite if and only if it is compact and totally discontinuous and its group of inner automorphism is relatively compact in its homeomorphism group.
