3 ms·
Invariants are useful because they allow you to distinguish equivalent knots, which is otherwise really hard to do. If two knots have different invariants, then
by Varinius 10y ago
Invariants are useful because they allow you to distinguish equivalent knots, which is otherwise really hard to do. If two knots have different invariants, then they are surely different.
Dually, you would want the following: if two knots have identical dinvariants, then they are surely the same. Since "if the knots are equivalent, the assigned values might not be equal", dinvariants cannot accomplish this function, and that makes them mostly useless.
(full disclosure: lawyer who did his undergraduate degree in math, not a topologist)
- wolfgke 10y ago> Invariants are useful because they allow you to distinguish equivalent knots, which is otherwise really hard to do. If two knots have different invariants, then they are surely different. > if two knots have identical dinvariants, then they are surely the same. Since "if the knots are equivalent, the assigned values might not be equal", dinvariants cannot accomplish this function, and that makes them mostly useless. That doesn't make them useless. Dinvariants just serve a different purpose: - invariants serve the purpose of distinguishing knots that are different - dinvariants serve the purpose of detecting that knots that look very different are actually the same