SO-type super-A-polynomial branch conjecture

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Let KK be a knot satisfying the exponential growth property. Let ASO⁡(K;x,y,a,t)\mathscr{A}^{\operatorname{SO}}(K;x,y,a,t) be the SO-type super-AA-polynomial, and let ASO⁡(K;x,y,a)A^{\operatorname{SO}}(K;x,y,a) and ASU⁡(K;x,y,a)A^{\operatorname{SU}}(K;x,y,a) be the SO- and SU-type aa-deformed AA-polynomials.

SO-type super-A-polynomial branch conjecture. At t=−1t=-1, the zero locus

ASO⁡(K;x,y,a,t=−1)=0\mathscr{A}^{\operatorname{SO}}(K;x,y,a,t=-1)=0

includes the two branches

ASO⁡(K;x,y,a)=0A^{\operatorname{SO}}(K;x,y,a)=0

and

ASU⁡(K;x,y,a)=0.A^{\operatorname{SU}}(K;x,y,a)=0.

The claim identifies both classical SO- and SU-type branches inside the decategorified SO-type super-AA-polynomial; the supplied text does not give a resolution status.

References

Primary source

Hao Ellery Wang, Yuanzhe Jack Yang, Hao Derrick Zhang and Satoshi Nawata, “On knots, complements, and 6j-symbols”, arXiv:2012.12008 (2021).

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