Three examples of applied and computational homology

Computational algebraic topology has already existed for some decades, with as its main objective the generation of examples. Nowadays, the field is rapidly changing into an applied branch of mathematics that is important in its own right. Robert Ghrist, topologist at the University of Illinois and one of the winners of the 2007 Scientific American 50 award, gives us three examples that illustrate this development, each with a different origin.