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- W4310628699 abstract "We generalize the combinatorial approaches of Rapaport and Higgins--Lyndon to the Whitehead algorithm. We show that for every automorphism $varphi$ of a free group $F$ and every word $uin F$ there exists a finite multiset of words $S_{u,varphi}$ satisfying the following property: For every cyclic word $w$, the number of times $u$ appears as a subword of $varphileft(wright)$ depends only on the appearances of words in $S_{u,varphi}$ as subwords of $w$. We use this fact to construct a faithful representation of $text{Out}left(F_{n}right)$ on an inverse limit of $mathbb{Z}$-modules, so that each automorphism is represented by sequence of finite rectangular matrices, which can be seen as successively better approximations of the automorphism." @default.
- W4310628699 created "2022-12-13" @default.
- W4310628699 creator A5008944176 @default.
- W4310628699 date "2022-11-30" @default.
- W4310628699 modified "2023-10-16" @default.
- W4310628699 title "A representation of $text{Out}left(F_{n}right)$ by counting subwords of cyclic words" @default.
- W4310628699 doi "https://doi.org/10.48550/arxiv.2212.00123" @default.
- W4310628699 hasPublicationYear "2022" @default.
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