  We discuss evolution of the Fermi surface (FS) topology with doping in
electron doped cuprates within the framework of a one-band Hubbard Hamiltonian,
where antiferromagnetism and superconductivity are assumed to coexist in a
uniform phase. In the lightly doped insulator, the FS consists of electron
pockets around the $(\pi,0)$ points. The first change in the FS topology occurs
in the optimally doped region when an additional hole pocket appears at the
nodal point. The second change in topology takes place in the overdoped regime
($\sim18%$) where antiferromagnetism disappears and a large
$(\pi,\pi)$-centered metallic FS is formed. Evidence for these two topological
transitions is found in recent Hall effect and penetration depth experiments on
Pr$_{2-x}$Ce$_{x}$CuO$_{4-\delta}$ (PCCO) and with a number of spectroscopic
measurements on Nd$_{2-x}$Ce$_{x}$CuO$_{4-\delta}$ (NCCO).
