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Which 3-manifold groups are Kähler groups?

Alexandru Dimca, Alexander Suciu (2009)

Journal of the European Mathematical Society

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 .

Word distance on the discrete Heisenberg group

Sébastien Blachère (2003)

Colloquium Mathematicae

We establish an exact formula for the word distance on the discrete Heisenberg group ℍ₃ with its standard set of generators. This formula is then used to prove the almost connectedness of the spheres for this distance.

W-perfect groups

Selami Ercan (2015)

Open Mathematics

In the present article we define W-paths of elements in a W-perfect group as a useful tools and obtain their basic properties.

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