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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2004 • Question 16

Question

Math 6510 • Differentiable Manifolds Fall 2004 • Question 16

Let \(X\) be the space obtained by attaching a disk \(D\) to \(S^1\times S^1\) where the attaching map is a degree \(d\) map from \(\partial D\) to \(S^1\times \{pt\}\). Calculate the homology and cohomology groups for \(X\) with \(\mathbb {Z}\) and \(\mathbb {Z}_p\) coefficients where \(p\) is prime.

Raw LaTeX

Let \(X\) be the space obtained by attaching a disk \(D\) to \(S^1\times S^1\) where
the attaching map is a degree \(d\) map from \(\partial D\) to \(S^1\times\{pt\}\). Calculate
the homology and cohomology groups for \(X\) with \(\mathbb{Z}\) and \(\mathbb{Z}_p\)
coefficients where \(p\) is prime.

Topic Tags

CW Complexes and Cell Attachments Cohomology and Cup Products Homology with Coefficients Homotopy and Degree on Manifolds