Using a topological approach, we study the dynamics of the basement me
mbrane of the mammalian epidermis when basal cells detach or divide. A
theoretical characterization of the steady state of the tissue, in ve
ry good agreement with experimental data, includes for the first time
the division and the disappearance of cells in a two-dimensional rando
m cellular structure. We predict a strong correlation between the size
of the attachment of basal cells to the basement membrane and their b
iological behavior (division or detachment). This suggests that the ma
in factor determining the fate of basal cells, and thus controlling th
e renewal of the epidermis, is the cells' surface tension and adhesion
.