Homology (and Cohomology) are one of the key methodical innovations in pure Mathematics in the 20th century. It started as the topological concept described in the article, but the core idas apply much more general.
Todays: Algebraic Geometry, Number Theory, Category Theory, Singularity Theory, String Theory, etc. are full of "cohomology". There are thousands of different flavours in use, that measure different properties of "spaces" of interest.
Much of category theory was initially created to deal with "complexes of abelian objects" that are used to define cohomology theories.
Working with cohomology was my bread and butter, when working as a mathematician. I always hoped to apply sone idas to Computer Science as well, when I entered the field, but I did not find any sane ways to make use of that "technology". E.g. homology of graphs is pretty boring, since they are only 1dimensional.
Is anyone aware of any CS applications of Homology?
Much of category theory was initially created to deal with "complexes of abelian objects" that are used to define cohomology theories.
Working with cohomology was my bread and butter, when working as a mathematician. I always hoped to apply sone idas to Computer Science as well, when I entered the field, but I did not find any sane ways to make use of that "technology". E.g. homology of graphs is pretty boring, since they are only 1dimensional. Is anyone aware of any CS applications of Homology?