Ideal Turaev-Viro invariants
| dc.creator | King, Simon A. | |
| dc.date | 2005-09-08 | |
| dc.date.accessioned | 2026-07-07T08:07:17Z | |
| dc.date.available | 2026-07-07T08:07:17Z | |
| dc.description | A Turaev-Viro invariant is a state sum, i.e., a polynomial that can be read off from a special spine or a triangulation of a compact 3-manifold. If the polynomial is evaluated at the solution of a certain system of polynomial equations (Biedenharn-Elliott equations) then the result is a homeomorphism invariant of the manifold (``numerical Turaev-Viro invariant''). The equation system defines an ideal, and actually the coset of the polynomial with respect to that ideal is a homeomorphism invariant as well (``ideal Turaev-Viro invariant''). It is clear that ideal Turaev-Viro invariants are at least as strong as numerical Turaev-Viro invariants, and we show that there is reason to expect that they are strictly stronger. They offer a more unified approach, since many numerical Turaev-Viro invariants can be captured in a singly ideal Turaev-Viro invariant. Using computer algebra, we obtain computational results on some examples of ideal Turaev-Viro invariants. | |
| dc.description | 16 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0509187 | |
| dc.identifier | http://arxiv.org/abs/math/0509187 | |
| dc.identifier | Topology and Its Applications 154 (2007), pp. 1141-1156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130889 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Commutative Algebra | |
| dc.subject | 57M27 (Primary); 13P10, 57-04 (Secondary) | |
| dc.title | Ideal Turaev-Viro invariants | |
| dc.type | text |