Finite Type Invariants , the Mapping Class Group and Blinks

Motivated by the lower central series of three important subgroups of the mapping class group, and by the recent ideas of p-branes in string theory, we introduce a notion of blinks and BL-type invariants of oriented integral homology 3-spheres. In the rst part of the paper we show that the ltrations (on the vector space generated by oriented integral homology 3-spheres) coming from these subgroups of the mapping class group coincide with ones coming from links, blinks and boundary links. In the second part, we show that the notions (based on algebraically split links, boundary links and blinks) of nite type invariants of integral homology 3-spheres are all equivalent, thus deducing a relation between nite type invariants and the I-adic completion of subgroups of the mapping class group. In the third part, we relate the notions of blink surgery equivalence to the notion of Seifert matrix of blinks.