Abstract
We describe several applications of the explicit formulas for SU(2) and SO(3) quantum invariants τr and ξr of lens spaces in [LL]. By using formulas for τ2 and ξ3 we derive a formula of the Rademacher Φ function mod 24, which appears in the transformation of Dedekind η function under the modular group PSL(2, Z). Via τ3, Brown invariants of lens spaces, as well as μ invariants of lens spaces mod 8, are presented in terms of Jacobi symbols. Formulas for μ−invariants of lens spaces involving the Φ function are also given.
| Original language | English (US) |
|---|---|
| Title of host publication | Frontiers in Differential Geometry, Partial Differential Equations, and Mathematical Physics |
| Subtitle of host publication | In Memory of Gu Chaohao |
| Publisher | World Scientific Publishing Co. |
| Pages | 169-187 |
| Number of pages | 19 |
| ISBN (Electronic) | 9789814578097 |
| ISBN (Print) | 9789814578073 |
| DOIs | |
| State | Published - Jan 1 2014 |