In a post on his weblog, Michael Greinecker mentioned some applications of homology to economics. While aimlessly websurfing for more information, I came across the homepage of Graciela Chichilnisky, a mathematical economist who has extensively applied topological techniques to economic questions. Chichilnisky has written nearly 200 articles, and includes PDFs on her site.
On a less happy note, Chichilnisky also links to a site dedicated to detailing her problems with Columbia University, where she is a tenured professor. Chichilnisky had successfully sued Columbia on the grounds of sex discrimination in the 90s. The two parties are now back in court over an alleged pattern of retaliation on the part of Columbia. An article on her experiences with the reviewing process also makes depressing reading.