Existence of the augmentation polynomial for every knot
Existence of the augmentation polynomial for every knot
Let be a knot. The augmentation variety is the set of augmentation values in , and the augmentation polynomial is defined when the maximal-dimensional part of the Zariski closure of has codimension . Existence conjecture. The condition about this Zariski closure holds for every knot , so the augmentation polynomial is always defined. This asserts universal existence of the three-variable augmentation polynomial, beyond the cases where it has been explicitly computed.
Sources & referencesView supporting material
Primary source
Lenhard Ng, “A topological introduction to knot contact homology”, arXiv:1210.4803 (2014).
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