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010 a| 2023031264;

020 a| 9781470463120q| (paperback);

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035 a| (WaSeSS)ssj0002880385;

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049 a| EREEa| NEHH;

050 00 a| QA612.14b| .H83 2023;

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084 a| 57M50a| 32G152| msc;

100 1 a| Huang, Yi,d| 1986-?| UNAUTHORIZED;

245 10 a| Mcshane identities for higher Teichmüller theory and the Goncharov-Shen potentialh| [electronic resource] /c| Yi Huang, Zhe Sun.;

260 a| Providence, RI :b| American Mathematical Society,c| 2023.;

300 a| v, 116 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 286, number 1422;

504 a| Includes bibliographical references (pages 113-116).;

505 0 a| Preliminary -- Properties of projective invariants -- Goncharov-Shen potentials -- Identities for PGL3(R)-representations with unipotent boundary -- Simple geodesic sparsity for convex real projective surfaces -- McShane identities for higher Teichmuller space -- Applications.;

506 a| Available only to authorized users.;

520 a| "We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen, which generalize the notion of horocycle lengths. In particular, we obtain McShane-type identities for finite-area cusped convex real projective surfaces by generalizing the Birman-Series geodesic scarcity theorem. More generally, we establish McShane-type identities for positive surface group representations with loxodromic boundary monodromy, as well as McShanetype inequalities for general rank positive representations with unipotent boundary monodromy. Our identities are systematically expressed in terms of projective invariants, and we study these invariants: we establish boundedness and Fuchsian rigidity results for triple and cross ratios. We apply our identities to derive the simple spectral discreteness of unipotent-bordered positive representations, collar lemmas, and generalizations of the Thurston metric"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Low-dimensional topology.=| ^A206151;

650 0 a| Teichmüller spaces.=| ^A81444;

650 0 a| Potential theory (Mathematics)=| ^A19374;

650 0 a| Combinatorial identities.=| ^A123016;

650 0 a| Geodesics (Mathematics)=| ^A283230;

650 0 a| Convex surfaces.=| ^A98148;

650 0 a| Cusp forms (Mathematics)=| ^A186974;

650 7 a| Manifolds and cell complexes -- Low-dimensional topology -- Geometric structures on low-dimensional manifolds.2| msc;

650 7 a| Several complex variables and analytic spaces -- Deformations of analytic structures -- Moduli of Riemann surfaces, Teichmüller theory.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Sun, Zhec| (Researcher in geometric topology)?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30627614;

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Mcshane identities for higher Teichmüller theory and the Goncharov-Shen potential / Yi Huang, Zhe Sun.

Author/creator	Huang, Yi, 1986-
Other author	Sun, Zhe (Researcher in geometric topology)
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2023.
Description	v, 116 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Low-dimensional topology. Teichmüller spaces. Potential theory (Mathematics) Combinatorial identities. Geodesics (Mathematics) Convex surfaces. Cusp forms (Mathematics)

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 286, number 1422
Contents	Preliminary -- Properties of projective invariants -- Goncharov-Shen potentials -- Identities for PGL3(R)-representations with unipotent boundary -- Simple geodesic sparsity for convex real projective surfaces -- McShane identities for higher Teichmuller space -- Applications.
Abstract	"We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen, which generalize the notion of horocycle lengths. In particular, we obtain McShane-type identities for finite-area cusped convex real projective surfaces by generalizing the Birman-Series geodesic scarcity theorem. More generally, we establish McShane-type identities for positive surface group representations with loxodromic boundary monodromy, as well as McShanetype inequalities for general rank positive representations with unipotent boundary monodromy. Our identities are systematically expressed in terms of projective invariants, and we study these invariants: we establish boundedness and Fuchsian rigidity results for triple and cross ratios. We apply our identities to derive the simple spectral discreteness of unipotent-bordered positive representations, collar lemmas, and generalizations of the Thurston metric"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 113-116).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023031264
ISBN	9781470463120 (paperback)
ISBN	(pdf)

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Mcshane identities for higher Teichmüller theory and the Goncharov-Shen potential / Yi Huang, Zhe Sun.

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