A General Local-to-Global Principle for Convexity of Momentum Maps

Details A General Local-to-Global Principle for Convexity of Momentum Maps A General Local-to-Global Principle for Convexity of Momentum Maps

2010-09-13

arxiv.org/abs/1009.2527v2

Mathematics

Symplectic Geometry

19 pages LaTeX2e, Preprint 2009, see also: Convexity of Momentum Maps: A Topological Analysis, several parts of the content we

Scientific paper

We extend the Local-to-Global-Principle used in the proof of convexity theorems for momentum maps to not necessarily closed maps whose target space carries a convexity structure which need not be based on a metric. Using a new factorization of the momentum map, convexity of its image is proved without local fiber connectedness, and for almost arbitrary spaces of definition. Geodesics are obtained by straightening rather than shortening of arcs, which allows a unified treatment and extension of previous convexity results.

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