The study extends the Bénard-Conway invariant equivalence to all two-component links with nonzero linking number, suggesting broader applicability of the result.
The Bnard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU.2/-representations of the link group with fixed meridional traces.For two-component links with linking number one, the invariant has been shown to equal a symmetrized multivariable link signature.We extend this result to all two-component links with nonzero linking number.A key ingredient in the proof is an explicit calculation of the Bnard-Conway invariant for .2 ; 2`/-torus links with the help of Chebyshev polynomials.
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Liu et al. (2026) studied this question.
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