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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2005 • Question 10

Question

Math 6510 • Differentiable Manifolds Fall 2005 • Question 10

Let \(T^2=S^1\times S^1\) be the standard 2-torus and \(p,q\in T^2\) be two distinct points. Let \(X=T^2/{\sim }\) be the identification space where the two points are identified \(p\sim q\). Find \(\pi _1(X)\).

Raw LaTeX

Let \(T^2=S^1\times S^1\) be the standard 2-torus and \(p,q\in T^2\) be two distinct
points. Let \(X=T^2/{\sim}\) be the identification space where the two points are
identified \(p\sim q\). Find \(\pi_1(X)\).

Topic Tags

Fundamental Groups Homotopy Groups Surface Topology and Surface Groups