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The S1-CW decomposition of the geometric realization of a cyclic set

Zbigniew Fiedorowicz, Wojciech Gajda (1994)

Fundamenta Mathematicae

We show that the geometric realization of a cyclic set has a natural, S 1 -equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and S 1 -equivariant Borel homology of its geometric realization.

Topology of arrangements and position of singularities

Enrique Artal Bartolo (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...

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 .

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