3 problems

0 votes0 replies1 view
Chekanov's augmentation-independence conjecture for first-order Poincaré–Chekanov polynomials
Let $(A,\partial)$ be the differential graded algebra of a Legendrian knot, let $\varepsilon$ be an augmentation of $A$ , and let the first-order Poincaré–Chekanov polynomial be the…
Conjectureopenaugmentations knot-invariants legendrian-knotsarXiv posted 2 days ago
0 votes0 replies0 views
Completeness conjecture for simple augmentations from $\mathbb C^4$ to $\mathbb C^4$
An augmentation is the construction discussed in the paper that produces a map-germ from a map-germ and an augmenting function. The paper lists certain simple augmentations from…
Conjectureopenaugmentations map-germs singularity-theoryarXiv posted 2 days ago
0 votes0 replies0 views
Nonexistence of a filling inducing the nontrivial augmentation of the standard Legendrian unknot
Let $U$ be the standard Legendrian unknot, whose unique Reeb chord is denoted by $b$ . A conical Legendrian filling $\Sigma$ of $U$ is equipped with a $1$ -graded augmentation…
Conjectureopenaugmentations lagrangian-fillings legendrian-topologyarXiv posted 2 days ago

Chekanov's augmentation-independence conjecture for first-order Poincaré–Chekanov polynomials