Algebraic Topology Allen Hatcher
Chapter 0
Chapter 2

Exercise 1.1
Exhibiting a Mobius strip a a quotient of a twosimplex

Exercise 1.4
Homology of the triangular parachute

Exercise 1.6
Another simplicial homology computation

Exercise 1.7
Exhibiting as a quotient of a tetrahedron

Exercise 1.8
A simplicial homology computation

Exercise 1.9
Computing the homology of when all faces of the same dimension are identified

Exercise 1.12
Chain homotopy of chain maps is an equivalence relation

Exercise 1.13
Chain homotopic maps remain chain homotopic when considering reduced homology

Exercise 1.14
Filling in arrows to make a short exact sequence

Exercise 1.16
The zero’th homology group of relative to is trivial precisely when meets each path component of

Exercise 1.17
A relative homology calculation for several spaces

Exercise 1.31
Exhibiting a case of the fivelemma, where the middle isomorphism is nonzero but all other maps are zero.

Exercise 2.2
Continuous maps have a point which is either fixed, or sent to its antipode

Exercise 2.3
A nonvanishing vector field on the solid ball has a point where it point radially outward, and another where it points radially inward

Exercise 2.4
Exhibiting a surjective map of degree zero

Exercise 2.9
Homology computations for several twodimensional CWcomplxes

Exercise 2.11
Homology computation for a certain space obtained from a 3cube under “twisted” face identifications

Exercise 2.28
Homology computations with MeyerVietoris

Exercise 2.29
Calculating the homology of the interiors of two copies of a 2surface identified along the 2surface itself

Exercise 2.31
Calculating homology of the suspension of a space
Chapter 3