Recently a promising start-up (Ayasdi) has made headlines. They are a spin-off of the Applied and Computational Algebraic Topology group of Stanford University (ComTop). What they basically do is visualizing the topological structure of Big Data.
Now I know that this idea of applied (algebraic) topology crops up from time to time also in finance, see e.g. this blog post from Quantivity: Manifold learning.
There is even an R-package with which you can play around (the concept behind it is persistent homology which is a robust variant of the topological invariant): Phom.
I am interested in applications of topological methods in finance, i.e. references (books, papers, articles) and software applications, that you can use to do some tests on your own.