Abstract:
We construct a combinatorial 1-cocycle for closed braids. When applied to the full rotation of the solid torus around its core it gives a Laurent polynomial which can sometimes detect the non-invertibility of the closed braid (what quantum invariants fail to do). In the case of knots in 3-space we use another type of 1-cocycles to introduce the tangle equations. If they have no solution, then the knots are not isotopic. On the other hand, each solution gives quantitative information about any isotopy which relates the two knots.
Language: English
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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