English

Convexity of Momentum Maps: A Topological Analysis

Symplectic Geometry 2012-02-14 v2 General Topology

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 ⁣:X\raYf\colon X\ra Y where the convexity structure of the target space YY need not be based on a metric. Using a new factorization of ff, convexity of the image is proved without local fiber connectedness, and for arbitrary connected spaces XX.

Keywords

Cite

@article{arxiv.1011.2266,
  title  = {Convexity of Momentum Maps: A Topological Analysis},
  author = {Wolfgang Rump and Jenny Santoso},
  journal= {arXiv preprint arXiv:1011.2266},
  year   = {2012}
}

Comments

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