Wolfgang Rump, Jenny Santoso
Convexity of Momentum Maps: A Topological Analysis
The paper is published: Topology Appl. 159 no. 5 (2012) 1288-1299

MSC:

52A01 Axiomatic and generalized convexity

53C23 Global topological methods (a la Gromov)

54C10 Special maps on topological spaces (open, closed, perfect, etc.)

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

70H05 Hamilton's equations

54E18 $p$-spaces, $M$-spaces, $sigma$-spaces, etc.

Abstract: We extend the Local-to-Global-Principle used in the proof of convexity theorems
for momentum maps to not necessarily closed maps $f\colon X\ra Y$ whose target space $Y$ carries a convexity structure which need not
be based on a metric. Using a new factorization of $f$, convexity of
its image is proved without local fiber connectedness, and for almost arbitrary spaces $X$.

Keywords: Convexity space, geodesic manifold, momentum map, Lokal-global-Prinzip