Let \(M\) be a 3-manifold such that for every compact set \(K\subset M\) there is a solid torus \(W\subset M\) with \(K\subset W\). Show that \(\pi _1(M)=\mathbb {Z}\) or \(0\).
Question
Math 6510 • Differentiable Manifolds
Winter 2004 • Question 12
Question
Winter 2004 • Question 12
Let \(M\) be a 3-manifold such that for every compact set \(K\subset M\) there is a solid torus \(W\subset M\) with \(K\subset W\). Show that \(\pi _1(M)=\mathbb {Z}\) or \(0\).