Why is it interesting?

Homology theory is perhaps the most profound and far reaching creation in all topology.

S. Lefschetz

Layman

The homology of a space is one of the simplest examples of a general class of mathematical constructions called topological invariants. A topological invariant is something that doesn't change as one deforms a space, and thus only depends on its topology. A good topological invariant allows a topologist to tell if two different spaces can be deformed into each other or are truly distinct. Just compute the topological invariants of the two spaces and, if they are different, the spaces certainly cannot be deformed one into the other. A topological invariant associated to a space may simply be a number, but it can also be something more complicated.

page 133 in Not Even Wrong by Peter Woit

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Researcher

Examples

Example1

Example2:

FAQ

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