Let \(A\subseteq X\) and let \(r:X\to A\) be a retraction. Prove that \[ r_*:\pi_1(X)\to\pi_1(A) \] is surjective.
A retraction induces a surjection on fundamental groups
P-TOP-WORKSHOP-HR-W1
- Area
- Topology
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- draft
P-TOP-WORKSHOP-HR-W1
Let \(A\subseteq X\) and let \(r:X\to A\) be a retraction. Prove that \[ r_*:\pi_1(X)\to\pi_1(A) \] is surjective.