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by A Beliakova, I Bühler, T T Q Le

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by
Anna Beliakova, Thang Le

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...nsky). Recently, Habiro ring found applications in algebraic geometry for constructing varieties over the non–existing field of one element [15]. Unified invariants of rational homology 3–spheres. In =-=[2]-=-, we give a full generalization of the Habiro theory to rational homology 3–spheres. This requires completely new techniques coming from number theory, commutative algebra, quantum group and knot theo...

by
Anna Beliakova, Qi Chen, Thang Le

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... (εm) ′ km ⊗Vs1⊗···⊗Vsl q (JT ) . Here P (ε)′ k = P (ε) k /{k}! . ON THE INTEGRALITY OF THE WRT INVARIANTS 29 Without loss of generality, we may assume k1 = k = max(k1, . . . , km). By Theorem A.3 in =-=[BBuL]-=-, (id⊗m⊗ trVs1q ⊗ · · · ⊗ trVslq )(JT ) ∈ qa (˜U⊗(e)q )inv, for some a ∈ 1 4 Z. Let y := (id⊗ trP (ε2) ′ k2 q ⊗ · · · ⊗ trP (εm) ′ km q ⊗ trVs1q ⊗ · · · ⊗ trVslq )(JT ) . Then cL⊔L′(k) = tr P (ε1) ′ k...

by
Takahito Kuriya

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...shed yet. The first author [21] showed a proof, but his proof is partially incomplete. The aim of this paper is to show a complete proof of the theorem. 2 For rational homology 3-spheres, it is known =-=[9]-=- that the quantum WRT invariant τ SO(3) r (M), at roots of unity of order co-prime to the order of the first homology group, can be obtained from the perturbative invariant τsl2(M). Hence, the LMO inv...

by
Takahito Kuriya, Thang T. Q. Le, Tomotada Ohtsuki
, 2010

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