Signatures of TQFTs and trace fields of two-bridge knots
Abstract
Let 0<s<r be coprime odd integers. We show that the Frobenius algebras governing the signatures of SO3 TQFTs at the root q=(iπ s /r) contain (and are often equal to) the trace field of the two-bridge knot of parameters (r,s). This gives an intriguing relationship between these two a priori unrelated objects of low-dimensional topology.
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