  A microscopic calculation of cross sections for fusion of oxygen isotopes
$^{16}$O, $^{22}$O and $^{24}$O is presented. Fermionic Molecular Dynamics wave
functions are used to describe the fully antisymmetrized and angular momentum
projected nucleus-nucleus system. The same effective nucleon-nucleon
interaction is used to determine the ground state properties of the nuclei as
well as the nucleus-nucleus interaction. From the microscopic many-body wave
function the corresponding wave function for the relative motion of two
point-like nuclei is derived by a method proposed by Friedrich which leads to a
local effective nucleus-nucleus potential. Finally the Schr{\"o}dinger equation
with incoming wave boundary conditions is solved to obtain the penetration
factors for the different partial waves. With these the S-factor for the fusion
process is calculated. A good agreement with experimental data is obtained for
the $^{16}$O-$^{16}$O cross section. Much enhanced cross sections are found for
the neutron-rich oxygen isotopes.
