McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential

Yi Huang Yau Mathematical Sciences Center Zhe Sun University of Science and Technology of China

Geometric Analysis and Geometric Topology Representation Theory mathscidoc:1905.15001

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 286, (1422), 2023.5
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 McShane-type 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.
Mcshane's identity, Fock–Goncharov A moduli space, Goncharov-Shen potential
[ Download ] [ 2019-05-15 17:04:25 uploaded by frease ] [ 1029 downloads ] [ 0 comments ]
@inproceedings{yi2023mcshane,
  title={McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential},
  author={Yi Huang, and Zhe Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190515170425465871345},
  booktitle={MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY},
  volume={286},
  number={1422},
  year={2023},
}
Yi Huang, and Zhe Sun. McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential. 2023. Vol. 286. In MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190515170425465871345.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved