Hatcher-Algebraic-Topology · Problem 2.2.10

Homology

Mathematics — Graph Theory · cellular-homology-computation

Problem

Let

X

be the quotient space of

S^2

under the identifications

x \sim -x

for

x

in the equator

S^1

. Compute the homology groups

H_i(X)

. Do the same for

S^3

with antipodal points of the equatorial

S^2 \subset S^3

identified.