Groups, Geometry, and Dynamics

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Volume 9, Issue 1, 2015, pp. 325–329
DOI: 10.4171/GGD/315

Published online: 2015-04-28

Thompson's group $F$ is not SCY

Stefan Friedl[1] and Stefano Vidussi[2]

(1) Universität Regensburg, Germany
(2) University of California, Riverside, United States

In this note we prove that Thompson's group $F$ cannot be the fundamental group of a symplectic 4-manifold with canonical class $K = 0 \in H^{2}(M)$ by showing that its Hausmann–Weinberger invariant $q(F)$ is strictly positive.

Keywords: Thompson's group, symplectic 4-manifolds

Friedl Stefan, Vidussi Stefano: Thompson's group $F$ is not SCY. Groups Geom. Dyn. 9 (2015), 325-329. doi: 10.4171/GGD/315