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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 18

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 18

Use the Mayer-Vietoris sequence to compute homology groups (with \(\mathbb {Z}\)-coefficients) of the space \(X_{2,3}\) from problem #17. Do the same for the space \(X_{2,2}\) defined similarly except that on \(S^1\times \{1\}\) antipodal points are identified.

Raw LaTeX

Use the Mayer-Vietoris sequence to compute homology groups (with
\(\Z\)-coefficients) of the space \(X_{2,3}\) from problem \#17. Do the same for the
space \(X_{2,2}\) defined similarly except that on \(S^1\times\{1\}\) antipodal points
are identified.

Topic Tags

Cellular Homology Homology with Coefficients Mayer-Vietoris Sequences Universal Coefficient Theorem