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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2016 • Question 13

Question

Math 6510 • Differentiable Manifolds Spring 2016 • Question 13

Let \(A\) be a retract of \(X\), and let \(i:A\to X\) be the inclusion. Prove that \(i_*:H_n(A)\to H_n(X)\) is injective for all \(n\).

Raw LaTeX

Let \(A\) be a retract of \(X\), and let \(i:A\to X\) be the inclusion. Prove
that \(i_*:H_n(A)\to H_n(X)\) is injective for all \(n\).

Topic Tags

Homology with Coefficients Homotopy Equivalence, Retracts, and Contractibility