Low dimensional projective groups

Indranil Biswas; Mahan Mj

Low dimensional projective groups

Geometric Topology 2014-02-27 v5 Algebraic Geometry

Authors: Indranil Biswas , Mahan Mj

Abstract

We initiate the study of holomorphically convex groups: groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers. If $G$ is a holomorphically convex group of cohomological dimension two, we show that $G$ is isomorphic to the fundamental group of a compact Riemann surface. As a consequence, we show that if a linear group $G$ has (rational) cohomological dimension two and is the fundamental group of a smooth complex projective variety, then $G$ is a (virtual) surface group.

Keywords

mapping class groups lie groups holonomy

Cite

@article{arxiv.1203.4520,
  title  = {Low dimensional projective groups},
  author = {Indranil Biswas and Mahan Mj},
  journal= {arXiv preprint arXiv:1203.4520},
  year   = {2014}
}

Comments

This paper is withdrawn due to a crucial gap in the proof of Theorem 4.7. This step in the proof goes through only in the presence of an extra cohomology vanishing condition

Low dimensional projective groups

Abstract

Keywords

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