On independent GKM-graphs without nontrivial extensions

Abstract

In this paper an example of a $k$-independent $(n,k)$-type GKM-graph without nontrivial extensions is constructed for any $n\ge k\ge 3$. It is shown that this example cannot be realized by a GKM-manifold for any $n=k=3$ or $n\ge k\ge 4$.

20 pages, 4 figures