Analytic asymptotic expansions of the Reshetikhin--Turaev invariants of Seifert 3-manifolds for SU(2)
| dc.creator | Hansen, Søren Kold | |
| dc.date | 2005-10-26 | |
| dc.date.accessioned | 2026-07-07T06:47:54Z | |
| dc.date.available | 2026-07-07T06:47:54Z | |
| dc.description | We calculate the large quantum level asymptotic expansion of the RT-invariants associated to SU(2) of all oriented Seifert 3-manifolds X with orientable base or non-orientable base with even genus. Moreover, we identify the Chern-Simons invariants of flat SU(2)-connections on X in the asymptotic formula thereby proving the so-called asymptotic expansion conjecture (AEC) due to J. E. Andersen for these manifolds. For the case of Seifert manifolds with base $S^2$ we actually prove a little weaker result, namely that the asymptotic formula has a form as predicted by the AEC but contains some extra terms which should be zero according to the AEC. We prove that these `extra' terms are indeed zero if the number of exceptional fibers n is less than 4 and conjecture that this is also the case if n is greater than 3. For the case of Seifert fibered rational homology spheres we identify the Casson-Walker invariant in the asymptotic formula. Our calculations demonstrate a general method for calculating the large r asymptotics of a finite sum $Σ_{k=1}^{r} f(k)$, where f is a meromorphic function depending on the integer parameter r and satisfying certain symmetries. Basically the method, which is due to L. Rozansky, is based on a limiting version of the Poisson summation formula together with an application of the steepest descent method from asymptotic analysis. | |
| dc.description | 107 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0510549 | |
| dc.identifier | http://arxiv.org/abs/math/0510549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103809 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 57M27 (Primary) 58J28, 41A60 (Secondary) | |
| dc.title | Analytic asymptotic expansions of the Reshetikhin--Turaev invariants of Seifert 3-manifolds for SU(2) | |
| dc.type | text |