Algebraic Topology · Problem 2.1.20

Homology — Allen Hatcher

Mathematics — Topology · suspension-homology

Problem

Show that

\widetilde{H}_n(X) \approx \widetilde{H}_{n+1}(SX)

for all

n

, where

SX

is the suspension of

X

. More generally, thinking of

SX

as the union of two cones

CX

with their bases identified, compute the reduced homology groups of the union of any finite number of cones

CX

with their bases identified.