A Pansiot-type subword complexity theorem for automorphisms of free groups
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866918043262648320 |
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| author | Hilion, Arnaud Levitt, Gilbert |
| author_facet | Hilion, Arnaud Levitt, Gilbert |
| contents | Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting laminations have complexity equivalent to n, n log log n, n log n, or n^2 (to n if the automorphism is fully irreducible). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_00676 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Pansiot-type subword complexity theorem for automorphisms of free groups Hilion, Arnaud Levitt, Gilbert Group Theory Combinatorics Dynamical Systems Geometric Topology Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting laminations have complexity equivalent to n, n log log n, n log n, or n^2 (to n if the automorphism is fully irreducible). |
| title | A Pansiot-type subword complexity theorem for automorphisms of free groups |
| topic | Group Theory Combinatorics Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2208.00676 |