具有2-挠率的同调3-球面的统一量子不变量及其加细
Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion
摘要：
对于每个只有2-挠率的有理同调3-球面，我们构造了一个统一的不变量（它取值于多项式环的某个分圆完备中），使得在任何奇数单位根单位根处对这个不变量的求值提供了在这个单位根处的SO（3）Witten-Reshetikhin-Turaev不变量，并且在任何偶数单位根单位根处提供了SU（2）量子不变量。此外，这个统一的不变量分裂成一个总和的细化统一的不变量主导的自旋和上同调细化的量子SU（2）不变量。Ohtsuki级数的新结果和量子不变量的完整性是我们构造的主要应用。
英文摘要：
For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction.
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