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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2003 • Question 13

Question

Math 6510 • Differentiable Manifolds Fall 2003 • Question 13

Compute the homology groups of the space obtained from a torus \(S^1\times S^1\) by attaching a Möbius band via a homeomorphism from the boundary circle of the Möbius band to the circle \(S^1\times \{x_0\}\) in the torus.

Raw LaTeX

Compute the homology groups of the space obtained from a torus \(S^1\times S^1\)
by attaching a M\"obius band via a homeomorphism from the boundary circle of the
M\"obius band to the circle \(S^1\times\{x_0\}\) in the torus.

Topic Tags

CW Complexes and Cell Attachments Homology with Coefficients Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups