Reduced Khovanov homology detects the unknot among prime knots

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Let UU denote the unknot, and let KK be a prime knot. Suppose that H^red(K){\widehat H}_{red}(K) and H^red(U){\widehat H}_{red}(U) are isomorphic as δ\delta-graded vector spaces over Z2\mathbb Z_2. Reduced Khovanov unknot-detection conjecture. Then

K=U.K=U.

This conjecture asks whether reduced Khovanov homology detects the unknot when restricted to prime knots. The surrounding discussion presents it as a natural problem; no resolution is supplied here.

References

Primary source

Zoltan Szabo, “A geometric spectral sequence in Khovanov homology”, arXiv:1010.4252 (2013).

Additional references

2 papers in this index state this conjecture (2006–2010). The statement above is taken from the most recent of them; the others are arXiv:math/0609531.

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