2020/04/05 by Guangming Hu, Hu, Guangming, Hideki Miyachi +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analytic and geometric function theory #Bone Metabolism and Diseases #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2004.02102
openalex publication_date 2020/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that every finitely unbranched covering α:\widetildeSg(α)→ S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Γα from the Teichmüller space T(S) to the Teichüller space T(\widetildeSg(α)). Actually, it has been showed that the isometric embedding Γα can be extended isometrically to the augmented Teichmüller space \widehatT(S) of T(S). Using this result, we construct a directed limit \widehatT∞(S) of augmented Teichmüller spaces, where the index runs over all finitely unbranched coverings of S. Then, we show that the action of the universal commensurability modular group Mod∞(S) can extend isometrically on \widehatT∞(S). Furthermore, for any X∞∈ T∞(S), its orbit of the action of the universal commensurability modular group Mod∞(S) on the universal commensurability augmented Teichmüller space \widehatT∞(S) is dense. Finally, we also construct a directed limit \widehatM∞(S) of augmented moduli spaces by characteristic towers and show that the subgroup Caut(π1(S)) of Mod∞(S) acts on \widehatT∞(S) to produce \widehatM∞(S) as the quotient.