The experimental method comparative genomic hybridization (CGH) array provides a full picture of chromosome amplifications and deletions of an individual's genome. The multi-dimensional nature of these data, however, has not been fully explored. Current methods for CGH analysis focus on specific markers, but deeper understanding can be gained by examining the properties of the overall genomic profile. In this paper we propose a novel method for characterizing CGH profiles mathematically using algebraic homology. We apply our method to breast cancer CGH profiles from patients that have been subjected to different treatments. We show that our results obtained using homology are in agreement with previous studies and are able to distinguish between frequency of cancer recurrence in chemotherapy and non-treated patient populations.