ABSTRACT
The present manuscript consists of three separate sections which deal with three different topics, though all of them are related to invariants of 3-manifolds. In the remainder of this section, we take r to be an odd prime, and suppose that M is a rational homology 3-sphere. This chapter provides an invariant of 3-manifolds from the universal Vassiliev-Kontsevich invariant, and show that it is related to the order of the homology group and the Casson invariant. Finite type invariants of knots were introduced by Vas-siliev. The chapter considers the composition of the coproducts and the linear map, and check that the image of the composition vanishes for each base of the center.
