Algebraic Topology · Problem 2.1.30

Homology — Allen Hatcher

Mathematics — Topology · commutative-diagrams

Problem

In each of the following commutative diagrams assume that all maps but one are isomorphisms. Show that the remaining map must be an isomorphism as well.

\begin{array}{ccc} A & \longrightarrow & B \\ \searrow & & \nearrow \\ & C & \end{array} \qquad \begin{array}{ccc} A & \longrightarrow & B \\ \downarrow & & \downarrow \\ C & \longrightarrow & D \end{array} \qquad \begin{array}{ccc} A & \longrightarrow & B \\ \downarrow & & \uparrow \\ C & \longrightarrow & D \end{array}

Browse the problem library