  Much progress has been made, and continues to be made, towards identifying
candidate mutated driver pathways in cancer. However, no systematic approach to
understanding how candidate pathways relate to each other for a given cancer
(such as Acute myeloid leukemia), and how one type of cancer may be similar or
different from another with regard to their respective pathways (Acute myeloid
leukemia vs. Glioblastoma multiforme for instance), has emerged thus far. Our
work attempts to contribute to the understanding of {\em space of pathways}
through a novel topological framework. We illustrate our approach, using
mutation data (obtained from TCGA) of two types of tumors: Acute myeloid
leukemia (AML) and Glioblastoma multiforme (GBM). We find that the space of
pathways for AML is homotopy equivalent to a sphere, while that of GBM is
equivalent to a genus-2 surface. We hope to trigger new types of questions
(i.e., allow for novel kinds of hypotheses) towards a more comprehensive grasp
of cancer.
