Some semigroups on a manifold with boundary

Abstract:

In this paper, $S$ is an abelian semigroup on an ${\text {n}}$-dimensional simply connected manifold with boundary whose interior is a dense, simply connected, connected Lie group. We also assume there is a vector semigroup $V_k^ -$ in $S$ such that the interior of $S$ misses the boundary of $V_k^ -$, and such that $(S - G{L_k})/{V_k}$ is a group. It is shown that if $k = n$, then $S$ is iseomorphic to $V_n^ -$, and if $k = 1,2$, or $n - 1$, then $S$ is iseomorphic to ${V_{n - k}} \times V_k^ -$.