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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2003 • Question 11

Question

Math 6510 • Differentiable Manifolds Fall 2003 • Question 11

Compute the fundamental group of the space obtained from two tori \(S^1\times S^1\) by identifying a circle \(S^1\times \{x_0\}\) in one torus with the corresponding circle \(S^1\times \{x_0\}\) in the other torus.

Raw LaTeX

Compute the fundamental group of the space obtained from two tori
\(S^1\times S^1\) by identifying a circle \(S^1\times\{x_0\}\) in one torus with the
corresponding circle \(S^1\times\{x_0\}\) in the other torus.

Topic Tags

Fundamental Groups Surface Topology and Surface Groups