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.|
|Number of pages||19|
|State||Published - Jan 1 2014|