On a Group Functor Describing Invariants of Algebraic Surfaces

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Date
2019-03-01MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2019,08Author
Dietrich, Heiko
Moravec, Primož
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Show full item recordOWP-2019-08
Abstract
Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of central extensions and Schur multipliers. In this work we relate $K$ and $\tilde K$ to a group functor $\tau$ arising in the construction of the non-abelian exterior square of a group. In contrast to $\tilde K$, there exist efficient algorithms for constructing $\tau$, especially for polycyclic groups. Supported by computations with the computer algebra system GAP, we investigate when $K(G,3)$ is a quotient of $\tau(G)$, and when $\tau(G)$ and $\tilde K(G,3)$ are isomorphic.