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Input data and context
% connected sum of two trefoils
s.l2.y1.y1.y1.u2
,1
% Fixed orientations: s.l2.y1.y1.y1.u2,0
Bar-Natan multicurve \(\mathrm{\widetilde{BN}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/connected_sum_3_1/cxBNr-c2-q', generated by kht++ v0.1-51-g2f7ea05 on Fri Feb 18 13:58:41 2022 GMT
1) h^6 q^12 δ^ 0 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<—
2) h^0 q^ 1 δ^1/2 ⬮——D—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯
Khovanov multicurve \(\mathrm{\widetilde{Kh}}(T)\)
options -c2-q
(diagram)
(metadata)
% file 'examples/strong_inversions/connected_sum_3_1/cxKhr-c2-q', generated by kht++ v0.1-51-g2f7ea05 on Fri Feb 18 13:58:41 2022 GMT
1) h^ 5 q^11 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^16 δ|^0
2) h^ 6 q^13 δ^1/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^18 δ|^0
3) h^ 3 q^ 9 δ^3/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^14 δ|^1
4) h^-1 q^ 3 δ^5/2 ⬯~~S~>⬮—>⬮~>⬮—>⬮~>⬯—>⬯<~⬮<—⬮<~⬮<—⬮<~⬯<— s4(0) q^8 δ|^2
5) h^-1 q^ 0 δ^ 1 ⬮~~S^2~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬮—>⬮~>⬯<—⬯<~⬮<—⬮<~⬮<—⬮<~⬮<—⬮<~⬮<— r(-1/8) q^80/9 δ|^1
Khovanov type D structure \(\mathrm{\widetilde{CKh}}(L)\)
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/connected_sum_3_1/cxCKh-c2', generated by kht++ v0.1-51-g2f7ea05 on Fri Feb 18 13:58:14 2022 GMT
1) h^0 q^ 4 δ^2 ⬮
2) h^2 q^ 8 δ^2 ⬮——H—>⬮
3) h^2 q^ 8 δ^2 ⬮——H—>⬮
4) h^4 q^12 δ^2 ⬮——H—>⬮
5) h^5 q^14 δ^2 ⬮——H—>⬮
Rasmussen's s-invariant
options -c2
(diagram)
(metadata)
% file 'examples/strong_inversions/connected_sum_3_1/cxCKh-c2', generated by kht++ v0.1-51-g2f7ea05 on Fri Feb 18 13:58:14 2022 GMT
4