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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2011 • Question 9

Question

Math 6510 • Differentiable Manifolds Spring 2011 • Question 9

Let \(X\) be a finite connected cell complex such that \(H^2(X;\mathbb {Z})=\mathbb {Z}/2\mathbb {Z}\) and \(H^i(X;\mathbb {Z})=0\) for \(i=1\) and \(i>2\). Compute \(H_i(X;\mathbb {Z})\) for all \(i\). State all theorems you are using.

Raw LaTeX

Let \(X\) be a finite connected cell complex such that \(H^2(X;\Z)=\Z/2\Z\) and
\(H^i(X;\Z)=0\) for \(i=1\) and \(i>2\). Compute \(H_i(X;\Z)\) for all \(i\). State all
theorems you are using.

Topic Tags

CW Complexes and Cell Attachments Cohomology and Cup Products Homology with Coefficients