arXiv subjects

Albert Marden

Publications and source records attributed to Albert Marden.

2 recordsLinked to original sources

arXiv2000

The monodromy groups of Schwarzian equations on closed Riemann surfaces

Let θ:π_1(R) \to \PSL(2,\C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem. Theorem. Necessary and sufficient for θto be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that θ(π_1(R)) be nonelementary. A branch point is required if and only if the representation θdoes not lift to \SL(2,\C).

math.CV↗

arXiv1998

Complex projective structures on Kleinian groups

Let M^3 be a compact, oriented, irreducible, and boundary incompressible 3-manifold. Assume that its fundamental group is without rank two abelian subgroups and its boundary is non-empty. We will show that every homomorphism from pi_1(M) to PSL(2,C) which is not `boundary elementary' is induced by a possibly branched complex projective structure on the boundary of a hyperbolic manifold homeomorphic to M.

math.GT↗