Groups, Geometry, and Dynamics

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Volume 2, Issue 2, 2008, pp. 245–261

DOI: 10.4171/GGD/38

Natural central extensions of groups

Christian Liedtke (1)

(1) Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstr. 1, 40225, DÜSSELDORF, GERMANY

Given a group G and an integer n ≥ 2 we construct a new group \tilde{\mathcal{K}}(G,n). Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of central extensions and the Schur multiplier. A surprising application is that Abelian groups of odd order possess naturally defined covers that can be computed from a given cover by a kind of warped Baer sum.

Keywords: Covering groups, Schur multiplier, fundamental groups of plane curve complements