N=4 - A UNIFYING FRAMEWORK FOR 2D TOPOLOGICAL GRAVITY, C(M)LESS-THAN-OR-EQUAL-TO-1 STRING THEORY AND CONSTRAINED TOPOLOGICAL SIGMA-MODEL

It is shown that two-dimensional (2d) topological gravity in the conformal gauge has a larger symmetry than has been hitherto recognized; in the formulation of Labastida, Pemici and Witten it contains a twisted ''small'' N = 4 superconformal symmetry. There are in fact two distinct twisted N = 2 structures within this N = 4, one of which is shown to be isomorphic to the algebra discussed by the Verlindes and the other corresponds, through bosonization, to c(M) less than or equal to 1 string theory discussed by Bershadsky et al. As a byproduct, we find a twisted N = 4 structure in c(M) less than or equal to 1 string theory. We also study the ''minor'' of this twisted N = 4 algebra and find that it corresponds, through another bosonization, to a constrained topological sigma model in complex dimension one.