Abstract
Any closed, orientable, smooth, nonpositively curved manifold M is known to admit a geometric characteristic splitting, analogous to the JSJ decomposition in three dimensions. We show that when this splitting consists of pieces which are Seifert fibered or pieces each of whose fundamental group has non-trivial centre, then M collapses with bounded curvature and has zero Perelman \({\bar{\lambda}}\) -invariant.
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Suárez-Serrato, P. Perelman’s \({\bar{\lambda}}\) -invariant and collapsing via geometric characteristic splittings. Geom Dedicata 147, 149–157 (2010). https://doi.org/10.1007/s10711-009-9446-2
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DOI: https://doi.org/10.1007/s10711-009-9446-2