论文标题
扭曲的伊瓦岛结的结
Twisted Iwasawa invariants of knots
论文作者
论文摘要
让$ p $为质量数字，整数$ $ m $ to $ p $。本着算术拓扑的精神，我们介绍了扭曲的Iwasawa不变性的概念$λ，μ，μ，$ {\ rm gl} _n $ -presentations和$ \ \ \ \ m athbb {z}/m \ m \ m \ m \ m \ m \ mathb {z} \ times \ times \ times \ mathbb {z} = $ _________-------------------------------- = $ _-_-_-cover。除其他事项外，我们的植川不变的一组决定了结的属和纤维，产生了它们的刚度刚度。附有几个直观的例子。我们进一步证明了$μ= 0 $定理，用于$ {\ rm sl} _2 $ - 扭曲组的表述，并提供一些评论。
Let $p$ be a prime number and $m$ an integer coprime to $p$. In the spirit of arithmetic topology, we introduce the notions of the twisted Iwasawa invariants $λ, μ, ν$ of ${\rm GL}_N$-representations and $\mathbb{Z}/m\mathbb{Z}\times \mathbb{Z}_p$-covers of knots. We prove among other things that the set of Iwasawa invariants determine the genus and the fiberedness of a knot, yielding their profinite rigidity. Several intuitive examples are attached. We further prove the $μ=0$ theorem for ${\rm SL}_2$-representations of twist knot groups and give some remarks.
