ABSTRACT
Quantum invariants for 3-manifolds associated with a compact Lie group were introduced by E. Witten using the Feynman integral. In the case of SU(2) they were mathematically defined by N. This chapter discusses the quantum Sp(2) invariants at eighth and tenth roots of unity by using G. Kuperberg’s graphical definition of the quantum Sp(2) invariant for links. Moreover we give topological interpretations of such invariants. Namely, the invariant at an eighth root of unity coincides with the quantum SU(2) invariant at a fourth root of unity, and so is determined by the Rochlin invariant, and the invariant at a tenth root of unity can be expressed in terms of the cohomology ring.
