Algebraic Topology · Problem 2.1.17

Homology — Allen Hatcher

Mathematics — Topology · relative-homology

Problem

(a) Compute the homology groups

H_n(X, A)

when

X

S^2

S^1 \times S^1

and

A

is a finite set of points in

X

. (b) Compute the groups

H_n(X, A)

and

H_n(X, B)

for

X

a closed orientable surface of genus two with

A

and

B

the circles shown. [What are

X/A

and

X/B