On the Quantum Invariant for the Brieskorn Homology Spheres
| dc.creator | Hikami, Kazuhiro | |
| dc.date | 2004-05-10 | |
| dc.date | 2005-01-01 | |
| dc.date.accessioned | 2026-07-07T06:23:14Z | |
| dc.date.available | 2026-07-07T06:23:14Z | |
| dc.description | We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres $Σ(p_1,p_2,p_3)$ by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit $τ\to N \in \mathbb{Z}$. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern-Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function. | |
| dc.description | 26 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0405028 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0405028 | |
| dc.identifier | Int. J. Math. 16, 661-685 (2005) | |
| dc.identifier | doi:10.1142/S0129167X05003004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96161 | |
| dc.subject | Mathematical Physics | |
| dc.title | On the Quantum Invariant for the Brieskorn Homology Spheres | |
| dc.type | text |