Covering space semigroups and retracts of compact Lie groups (Q506943)

Let \(B\) be a compact connected Lie group, \(N\) a finite central subgroup of \(B\) and \(f:B\to B/N\) be the quotient morphism of \(B\). The mapping cylinder \(MC(f)\) associated with \(f\) is a compact monoid called covering space semigroup. A covering space semigroup is not in general a manifold but it does admit a manifold boundary. The main theorem of this paper (Theorem 3.6) states that for a compact connected Lie group \(B\) having the central circle group as a direct factor there exist infinitely many covering space semigroups with \(B\) as a boundary, and each of them is a retract of \(B\).