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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2005 • Question 12

Question

Math 6510 • Differentiable Manifolds Winter 2005 • Question 12

Let \(X\) be the space obtained from two tori, \(S^1\times S^1\), by gluing \(S^1\times \{pt\}\) in one torus to \(S^1\times \{pt\}\) in the other torus with a degree two map. Calculate \(\pi _1(X)\).

Raw LaTeX

Let \(X\) be the space obtained from two tori, \(S^1\times S^1\), by gluing
\(S^1\times\{pt\}\) in one torus to \(S^1\times\{pt\}\) in the other torus with a degree
two map. Calculate \(\pi_1(X)\).

Topic Tags

Fundamental Groups Homotopy Groups Homotopy and Degree on Manifolds Surface Topology and Surface Groups