Splitting theorems for pro-p groups acting on pro-p trees

Pro-p groups acting on trees with finitely many maximal vertex stabilizers up to conjugation

“…Theorem 2.6. ( [10,Proposition 2.4] or [17,Theorem 9.6.1]) Let G be a pro-p group acting on a second countable (as a topological space) pro-p tree T with trivial edge stabilizers. Then there exists a continuous section σ : G\V (T ) −→ V (T ) and…”