Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2004 • Question 19

Question

Math 6510 • Differentiable Manifolds Winter 2004 • Question 19

Let \(X\) be a topological space obtained by adding a \(k\)-cell to \(\mathbb {C}P^n\). For what values \(i\) must \(H_i(X;\mathbb {Z})=H_i(\mathbb {C}P^n;\mathbb {Z})\)? What are the possibilities for \(H_i(X;\mathbb {Z})\) when the two groups are not equal?

Raw LaTeX

Let \(X\) be a topological space obtained by adding a \(k\)-cell to
\(\mathbb{C}P^n\). For what values \(i\) must
\(H_i(X;\mathbb{Z})=H_i(\mathbb{C}P^n;\mathbb{Z})\)? What are the possibilities for
\(H_i(X;\mathbb{Z})\) when the two groups are not equal?

Topic Tags

Homology with Coefficients Point-Set Topology and Separation Theorems