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We discuss the topological $CP^1$ model which consists of the holomorphicmaps from Riemann surfaces onto $CP^1$. We construct a large-$N$ matrix modelwhich reproduces precisely the partition function of the $CP^1$ model at allgenera of Riemann surfaces. The action of our matrix model has the form ${\rmTr}\, V(M)=-2{\rm Tr}\, M(\log M -1) +2\sum t_{n,P}{\rm Tr}\, M^n(\log M-c_n)+\sum 1/n\cdot t_{n-1,Q}{\rm Tr}\, M^n~(c_n=\sum_1^n 1/j )$ where $M$ is an$N\times N$ hermitian matrix and $t_{n,P}\, (t_{n,Q}),~(n=0,1,2,\cdots)$ arethe coupling constants of the $n$-th descendant of the puncture (K\"ahler)operator.Comment: 13 pages, LaTeX, UT-68

THE TOPOLOGICAL CP1 MODEL AND THE LARGE-N MATRIX INTEGRAL

THE TOPOLOGICAL CP¹ MODEL AND THE LARGE-N MATRIX INTEGRAL