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We have focused on the topological structure of Cubic string field theory(CSFT). From the similarity of action between CSFT and Chern-Simons (CS) theoryin three dimensions, we have investigated the quantity ${\cal N}=\pi^2/3\int(UQU^{-1})^3$, which is expected to be the counterpart of winding number in CStheory. In our previous research, it was reported that $\cal N$ can only take alimited number of integer values due to the inevitable anomalies in Okawa typesolution. To overcome this unsatisfactory results, we evaluate $\cal N$ and EOMagainst a solution itself, $\cal T$, for more general class of pure gauge formsolution written in $K,B$ and $c$ in this paper. Then we obtain general formulaof $\cal N$ and $\cal T$. From this result, we show that there is an infinitenumber of solutions that $\cal N$ takes any integer value while keeping $\calT=0$. We also show the gauge invariant observable of these solutions takeappropriate values. Furthermore, we evaluate the integral form of theBRST-exact quantity as surface integral.

Winding number for arbitrary integer value in Cubic String Field Theory