Which 3-manifold groups are Kähler groups?

Alexandru Dimca; Alexander Suciu

Journal of the European Mathematical Society (2009)

  • Volume: 011, Issue: 3, page 521-528
  • ISSN: 1435-9855

Abstract

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The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then G must be finite—and thus belongs to the well-known list of finite subgroups of O ( 4 ) , acting freely on S 3 .

How to cite

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Dimca, Alexandru, and Suciu, Alexander. "Which 3-manifold groups are Kähler groups?." Journal of the European Mathematical Society 011.3 (2009): 521-528. <http://eudml.org/doc/277585>.

@article{Dimca2009,
abstract = {The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if $G$ can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then $G$ must be finite—and thus belongs to the well-known list of finite subgroups of $\operatorname\{O\}(4)$, acting freely on $S^3$.},
author = {Dimca, Alexandru, Suciu, Alexander},
journal = {Journal of the European Mathematical Society},
keywords = {Kähler manifold; 3-manifold; fundamental group; cohomology ring; resonance variety; isotropic subspace; Kähler manifold; 3-manifold; fundamental group; cohomology ring; resonance variety; isotropic subspace},
language = {eng},
number = {3},
pages = {521-528},
publisher = {European Mathematical Society Publishing House},
title = {Which 3-manifold groups are Kähler groups?},
url = {http://eudml.org/doc/277585},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Dimca, Alexandru
AU - Suciu, Alexander
TI - Which 3-manifold groups are Kähler groups?
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 3
SP - 521
EP - 528
AB - The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if $G$ can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then $G$ must be finite—and thus belongs to the well-known list of finite subgroups of $\operatorname{O}(4)$, acting freely on $S^3$.
LA - eng
KW - Kähler manifold; 3-manifold; fundamental group; cohomology ring; resonance variety; isotropic subspace; Kähler manifold; 3-manifold; fundamental group; cohomology ring; resonance variety; isotropic subspace
UR - http://eudml.org/doc/277585
ER -

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