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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2011 • Question 8

Question

Math 6510 • Differentiable Manifolds Spring 2011 • Question 8

Let \(X\) denote the solid torus \(S^1\times D^2\). Using Mayer-Vietoris, compute the homology groups of the double of \(X\), obtained by taking two copies of \(X\) and gluing them along the boundary via the identity map. Also compute \(H_i(X,\partial X)\).

Raw LaTeX

Let \(X\) denote the solid torus \(S^1\times D^2\). Using Mayer-Vietoris,
compute the homology groups of the double of \(X\), obtained by taking two copies
of \(X\) and gluing them along the boundary via the identity map. Also compute
\(H_i(X,\partial X)\).

Topic Tags

Cellular Homology Homology with Coefficients Mayer-Vietoris Sequences Surface Topology and Surface Groups