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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1995 • Question 15

Question

Math 6510 • Differentiable Manifolds Fall 1995 • Question 15

In the product \(S^1\times S^1\) consider the subset \[ A:=S^1\times \{p\}\cup \{p\}\times S^1 \] where \(p\) is a point on \(S^1\). Calculate \(H_j(A,\mathbb {Z})\), \(j=0,1,2\).

Raw LaTeX

In the product \(S^1\times S^1\) consider the subset
\[
  A:=S^1\times\{p\}\cup\{p\}\times S^1
\]
where \(p\) is a point on \(S^1\). Calculate \(H_j(A,\mathbb{Z})\), \(j=0,1,2\).

Topic Tags

Cohomology and Cup Products Pullbacks and Wedge Products