Flexible exponents of non-geometric 3-manifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908995031138304 |
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| author | Lin, Jianfeng Sun, Hongbin Wang, Zhongzi |
| author_facet | Lin, Jianfeng Sun, Hongbin Wang, Zhongzi |
| contents | A classical question in quantitative topology is to bound the mapping degree $\operatorname{deg}(f)$ in terms of its Lipchitz constant $\text{Lip}(f)$. For a closed, orientable, Riemannian manifold $M$, the flexible exponent $α(M)$ is the infimum of $α\geqslant 0$ such that $|\text{deg}(f)|\leqslant C\cdot (\text{Lip}(f))^α$ holds for any Lipschitz map $f:M\to M$.
For a geometric 3-manifold $M$ in the sense of Thurston, $α(M)$ is determined in \cite{DLWWW}. In this paper, we determine $α(M)$ for non-geometric 3-manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flexible exponents of non-geometric 3-manifolds Lin, Jianfeng Sun, Hongbin Wang, Zhongzi Geometric Topology A classical question in quantitative topology is to bound the mapping degree $\operatorname{deg}(f)$ in terms of its Lipchitz constant $\text{Lip}(f)$. For a closed, orientable, Riemannian manifold $M$, the flexible exponent $α(M)$ is the infimum of $α\geqslant 0$ such that $|\text{deg}(f)|\leqslant C\cdot (\text{Lip}(f))^α$ holds for any Lipschitz map $f:M\to M$. For a geometric 3-manifold $M$ in the sense of Thurston, $α(M)$ is determined in \cite{DLWWW}. In this paper, we determine $α(M)$ for non-geometric 3-manifolds. |
| title | Flexible exponents of non-geometric 3-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2604.23965 |