  The post Gaussian effective potential in $D=2+2\veps$ dimensions is evaluated
for the Ginzburg-Landau theory of superconductivity. Two and three loop
integrals for the post Gaussian correction terms in $D=2+2\veps$ dimensions are
calculated and $\veps$-expansion for these integrals are constructed. In
$D=2+2\veps$ fractal dimensions Ginzburg Landau parameter turned out to be
sensitive to $\veps$ and the contribution of the post Gaussian term is larger
than that for D=3. Adjusting $\veps$ to the recent experimental data on $\kappa
(T)$ for high -$T_c$ cuprate superconductor $Tl_2Ca_2Ba_2Cu_3O_{10}
(T\cl-2223)$, we found that $\veps=0.21$ is the best choice for this material.
The result clearly shows that, in order to understand high - $T_c$
superconductivity, it is necessary to include the fluctuation contribution as
well as the contribution from the dimensionality of the sample. The method
gives a theoretical tool to estimate the effective dimensionality of the
samples.
