Perelman's invariant and collapse via geometric characteristic splittings

Details Perelman's invariant and collapse via geometric characteristic splittings Perelman's invariant and collapse via geometric characteristic splittings

2008-04-29

arxiv.org/abs/0804.4588v1

Mathematics

Differential Geometry

10 pages

Scientific paper

Any closed orientable and smooth non-positively 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, M collapses with bounded curvature and has zero Perelman invariant.

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