2010/11/10 by Wolfgang Rump, Rump, Wolfgang, Jenny Santoso +1
Mathematics · #52A01 #53C23 #53D20 (Primary) 54E18 (Secondary) #54C10 #FOS: Mathematics #General Topology (math.GN) #Symplectic Geometry (math.SG) #math.GN #math.SG #msc:52A01 #msc:53C23 #msc:53D20 #msc:54C10 #msc:54E18
paper · pdf · doi:10.48550/arxiv.1011.2266
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
arxiv created 2012/02/12 · arxiv updated 2012/02/14
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.