Entropy and domination for quasi-Hitchin representations

[2608.27939] Entropy and domination for quasi-Hitchin representations Skip to main content Search Submit Donate Log in Mathematics > Geometric Topology arXiv:2608.27939 (math) [Submitted on 28 Aug 2026 ( v1 ), last revised 23 Sep 2026 (this version, v2)] Title: Entropy and domination for quasi-Hitchin representations Authors: Pabitra Barman , Subhojoy Gupta View PDF HTML (experimental) Abstract: Let $S$ be a closed oriented surface of genus $g\geq 2$. We consider an $n$-pleated representation $\rho: \pi_1(S) \to \mathrm{PSL}_n(\mathbb{C})$ obtained by bending a Hitchin representation $\rho_0:\pi_1(S) \to \mathrm{PSL}_n(\mathbb{R})$ along a maximal geodesic lamination. The space of such $n$-pleated representations was recently introduced by Maloni-Martone-Mazzoli-Zhang who provided a parametrization via shear-bend cocycles. Our main result is that $\rho_0$ dominates $\rho$ in the Hilbert length spectrum and the translation-length spectrum, with a strict domination for $\textit{most}$ curves, that we call $\textit{statistical}$ domination. Using this, we prove some entropy rigidity results: namely, the Hilbert entropy of any quasi-Hitchin representation in the bending fiber is strictly greater than that of $\rho_0$, the same for the translation length entropy when $\rho_0$ is $n$-Fuchsian, and in the latter case a new proof that for hyperconvex representations the Hausdorff dimension of the full limit set increases. The proof involves analyzing the weighted planar networks for finite approximants of the monodromy matrix, and establishing a strict matrix domination for generic monodromy using the equidistribution of closed geodesics in the unit tangent bundle of $S$. Comments: 49 pages, 6 figures. v2 has various minor improvements and organizational changes Subjects: Geometric Topology (math.GT) MSC classes: 57K20, 20H10 Cite as: arXiv:2608.27939 [math.GT] (or arXiv:2608.27939v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2608.27939 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Subhojoy Gupta [ view email ] [v1] Fri, 28 Aug 2026 05:27:25 UTC (207 KB) [v2] Wed, 23 Sep 2026 10:10:58 UTC (228 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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