m at h . Q A ] 2 7 Ju l 1 99 8 Kirby - Melvin ’ s τ ′ r and Ohtsuki ’ s τ for Lens Spaces
نویسنده
چکیده
Explicit formulae for τ ′ r(L(p, q)) and τ(L(p, q)) are obtained for all L(p, q). There are three systems of invariants of Witten-type for closed oriented 3manifolds: 1. {τr(M), r ≥ 2; τ ′ r(M), r odd ≥ 3}, where τr was defined by Reshetikhin and Turaev [1], and τ ′ r was defined by Kirby-Melvin [2] 2. {Θr(M,A), r ≥ 1,whereA is a 2r-th primitive root of unity} defined by Blanchet, Habegger, Masbamm and Vogel [3] 3. {ξr(M,A), r 6= 1, 4, 4k + 2, whereA is an r-th primitive root of unity} defined by the first author [4]. And it was proved in [4] that they are equivalent. Explicit formulae for {τr(M), r ≥ 2} and {ξr(M, er), r odd ≥ 3} have been obtained for lens spaces in [5], where ea = exp(2π √ −1/a). Ohtsuki [6] defined his invariant τ(M) = ∞
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