In this talk, I deal with to applications of computational homology
in biological systems. One of the most promising applications of homology to
the understanding of biological systems is that of persistent homology. The key
benets of using this method to describe data include coordinate-free descrip-
tion of shape, robustness in the presence of noise and invariance under many
transformations, as well as highly compressed representations of structures.
Recently, several applications of tools from algebraic topology to analyze
complex biological data from the domain of cancer research have been reported.
In this talk, I describe some methods which are used nowadays in progression
analysis of cancer. I imply how the homological properties of simplicial com-
plexes give information about progression of a sarcoma.