Reference : McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/39494
McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential
English
Sun, Zhe mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Huang, Yi mailto [Yau Mathematical Sciences Center]
Jan-2019
89
No
[en] Mcshane's identity ; Fock–Goncharov A moduli space ; Goncharov-Shen potential
[en] In [GS15], Goncharov and Shen introduce a family of mapping class group invariant regular functions on their A-moduli space to explicitly formulate a particular homological mirror symmetry conjecture. Using these regular functions, we obtain McShane identities general rank positive surface group representations with loxodromic boundary monodromy and (non-strict) McShane-type inequalities for general rank positive representations with unipotent boundary monodromy. Our identities are expressed in terms of projective invariants, and we study these invariants: we establish boundedness and Fuchsian rigidity results for triple ratios. Moreover, we obtain McShane identities for finite-area cusped convex real projective surfaces by generalizing the Birman--Series geodesic scarcity theorem. We apply our identities to derive the simple spectral discreteness of unipotent bordered positive representations, collar lemmas, and generalizations of the Thurston metric.
http://hdl.handle.net/10993/39494
https://arxiv.org/abs/1901.02032
FnR ; FNR13242285 > Zhe Sun > > COmbinatorial and ALgebraic Aspects of Surface group representations. > 01/09/2018 > 31/08/2020 > 2017

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
MCLGv8.pdf89 pages, 25 figures.Publisher postprint1.57 MBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.