arXiv subjects

Jenny Santoso

Publications and source records attributed to Jenny Santoso.

2 recordsLinked to original sources

arXiv2012

Convexity of Momentum Maps: A Topological Analysis

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 $X$.

math.SG↗

arXiv2010

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

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.

math.SG↗