Finite type 3-manifold invariants, the mapping class group and blinks

Abstract

The goal of the present paper is to find higher genus surgery formulas for the set of finite type invariants of integral homology 3-spheres, and to develop a theory of finite type invariants which will be applied in a subsequent publication [7] in the study of subgroups of the mapping class group. The main result is to show that six filtrations on the vector space generated by oriented integral homology 3-spheres (three coming from surgery on special classes of links and three coming from subgroups of the mapping class group) are equal. En route we introduce the notion of blink (a special case of a link) and of a new subgroup of the mapping class group. © 1997 Journal of Differential Geometry. © 1997 Applied Probability Trust.