Convexity of Momentum Maps: A Topological Analysis

Abstract

The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps $f\colon X\ra Y$ where the convexity structure of the target space $Y$ need not be based on a metric. Using a new factorization of $f$, convexity of the image is proved without local fiber connectedness, and for arbitrary connected spaces $X$.

21 pages LaTeX2e; minor revisions, to appear in Topology and its Applications; Dedicated to Alan D. Weinstein, Dennis P. Sullivan, and in memory of Jerrold E. Marsden. arXiv admin note: substantial text overlap with arXiv:1009.2527