homology

[Liu]

I finally finished reading the first section of Chapter two of the
book:”Algebraic topology” written by Allen Hatcher. The idea of Delta-
complexes is something between simplicial complex and CW complex. It
surly makes things easier to compute, yet harder to understand.
(always a paradox) All the materials here are basic. I got confused at
the sign “\patial” for some time, because it sometimes denotes the
boundary homomorphism and boundary of a space other times. In order to
prove the Homotopy invariance of Homology, the introduction of prism
operators is presented much clearer than the textbooks I met before.
Excision Theorem is quite an important one. The book takes more than
five pages to prove it and when this is done, the whole section is
near its end.

There is also a concept that “local homology” which appears later in
this section. A friend of mine is trying to understand the concept
“local cohomology”, a concept in algebraic geometry, which has
something to do with sheaf theory. But here I can’t see any connection
with these two definitions. I will read more about them, though.