Let \(\Sigma _2\) be a closed, orientable surface of genus 2. Prove that \(\pi _1(\Sigma _2)\) has a normal subgroup \(G\) such that \(\pi _1(\Sigma _2)/G\cong \mathbb {Z}\).
Question
Math 6510 • Differentiable Manifolds
Spring 2018 • Question 10
Question
Spring 2018 • Question 10
Let \(\Sigma _2\) be a closed, orientable surface of genus 2. Prove that \(\pi _1(\Sigma _2)\) has a normal subgroup \(G\) such that \(\pi _1(\Sigma _2)/G\cong \mathbb {Z}\).