Recognizing a relatively hyperbolic group by its Dehn fillings
Recognizing a relatively hyperbolic group by its Dehn fillings
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通过 Dehn 填充识别相对双曲群
DOI：
10.1215/00127094-2018-0014
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发表时间：
2015
影响因子：
2.5
通讯作者：
Vincent Guirardel
中科院分区：
文献类型：
--
作者：
Franccois Dahmani;Vincent Guirardel
相对双曲群的Dehn填充推广了非紧双曲$3$-流形如双曲纽结补上的拓扑Dehn手术。我们证明了刚性的结果说，如果两个非初等相对双曲群没有合适的分裂有足够多的同构Dehn填充，那么这些群体实际上是同构的。我们的主要应用是一个解决方案的同构问题的类的非初等相对双曲群与剩余有限抛物群，并没有合适的分裂。
Dehn fillings for relatively hyperbolic groups generalize the topological Dehn surgery on a non-compact hyperbolic $3$-manifold such as a hyperbolic knot complement. We prove a rigidity result saying that if two non-elementary relatively hyperbolic groups without suitable splittings have sufficiently many isomorphic Dehn fillings, then these groups are in fact isomorphic. Our main application is a solution to the isomorphism problem in the class of non-elementary relatively hyperbolic groups with residually finite parabolic groups and with no suitable splittings.