There are many textbooks for
homology
of
simplicial complexes
and singular homology of topological spaces. It is
impossible to list all textbooks, each of which has
its own pros and cons. And singular homology is just
an example of a construction of one of
various homology theories
.
When I choose singular homology theory as a topic for
senior’s seminar (reading course), I ask hand a
list of important deﬁnitions and properties
concerning singluar homology theory to students and
ask them to go to the library and ﬁnd them.
Thus I don’t have any particular favorite
textbooks for elementary homology theory. I think,
however, it is a good idea to read
Dieudonné’s book
[
Die89
]
, which explains the process of sophistication from
Poincaré’s vague ideas into singular
homology theory and generalized homology theories.
