An Invariant of Integral Homology 3-Spheres Which Is Universal For All Finite Type Invariants
| dc.creator | Le, Thang T. Q. | |
| dc.date | 1996-01-02 | |
| dc.date | 1996-01-16 | |
| dc.date.accessioned | 2026-07-07T09:08:36Z | |
| dc.date.available | 2026-07-07T09:08:36Z | |
| dc.description | In [LMO] a 3-manifold invariant $Ω(M)$ is constructed using a modification of the Kontsevich integral and the Kirby calculus. The invariant $Ω$ takes values in a graded Hopf algebra of Feynman 3-valent graphs. Here we show that for homology 3-spheres the invariant $Ω$ is {\em universal} for all finite type invariants, i.e. $Ω_n$ is an invariant of order $3n$ which dominates all other invariants of the same order. This shows that the set of finite type invariants of homology 3-spheres is equivalent to the Hopf algebra of Feynman 3-valent graphs. Some corollaries are discussed. A theory of groups of homology 3-spheres, similar to Gusarov's theory for knots, is presented. | |
| dc.description | 23 pages, Amslatex; Typos and minor mistakes corrected; More explanations and details added; A stronger version of operations which do not change values of invariants up to some order is presented | |
| dc.identifier | https://arxiv.org/abs/q-alg/9601002 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9601002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150779 | |
| dc.subject | Quantum Algebra | |
| dc.title | An Invariant of Integral Homology 3-Spheres Which Is Universal For All Finite Type Invariants | |
| dc.type | text |