Algebraic Topology · Problem 4.1.16

Homotopy Theory — Allen Hatcher

Mathematics — Topology · factoring-maps-cw-complexes-homotopy-groups

Problem

Show that a map

f: X \to Y

between connected CW complexes factors as a composition

X \to Z_n \to Y

where the first map induces isomorphisms on

\pi_i

for

i \leq n

and the second map induces isomorphisms on

\pi_i

for

i \geq n + 1