Parametrizing Fuchsian Subgroups of the Bianchi Groups

DOI10.4153/CJM-1991-009-1zbMath0739.20020MaRDI QIDQ4713780

Alan W. Reid, Colin Maclachlan

Publication date: 25 June 1992

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Bianchi groupsquadratic formsPicard groupFuchsian subgroupsmaximal arithmetic Fuchsian groupsclosed immersed totally geodesic surfacecommensurability classes of arithmetic Fuchsian groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Structure of modular groups and generalizations; arithmetic groups (11F06) Linear algebraic groups over global fields and their integers (20G30) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (11)

Parametrizing Shimura subvarieties of \({\mathrm{A}_1}\) Shimura varieties and related geometric problems ⋮ Integral geometric orbifolds ⋮ On the growth of the number of primitive totally geodesic surfaces in some hyperbolic 3-manifolds ⋮ Totally geodesic hyperbolic 3-manifolds in hyperbolic link complements of tori in \(S^4\) ⋮ Fuchsian Subgroups of Bianchi Groups ⋮ Geometry of integral binary Hermitian forms ⋮ Geodesics with one self-intersection, and other stories ⋮ Compressing totally geodesic surfaces ⋮ Conjugacy classes of $SU(h,\mathcal O_S)$ in $SL(2,\mathcal O_S)$ ⋮ Counting immersed surfaces in hyperbolic 3-manifolds ⋮ On the arithmetic of cross-ratios and generalised Mertens' formulas

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