Finite type invariants, the mapping class group and blinks

Details Finite type invariants, the mapping class group and blinks Finite type invariants, the mapping class group and blinks

1997-12-17

arxiv.org/abs/q-alg/9712045v2

Mathematics

Quantum Algebra

51 pages, 44 figures, to be published in JDG. Replaced because of font problems in original

Scientific paper

The goal of the present paper is to find higher genus surgery formulae for the set of finite-type invariants of homology spheres, and to develop a companion theory of finite-type invariants to be applied, in a subsequent publication, to 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 homology 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.

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