3 ms·
The unknot isn't a prime knot for the same reason that 1 isn't a prime number.
by OscarCunningham 3y ago
The unknot isn't a prime knot for the same reason that 1 isn't a prime number.
- deleted 3y ago[deleted]
- Syzygies 3y agoYes. Alas, mathematicians not in number theory tend to have p-ness envy. A more troubling example of imposing this world view is decomposing 3-manifolds, where people like to think of S^1 x S^2 as prime. This only makes sense as a form of respect for one's elders. One constructs 3-manifolds by gluing irreducible manifolds together after cutting out balls; one needs S^3 itself to express self-loops in this gluing graph, if there are no other pieces. S^1 x S^2 is S^3 with one self-loop. But the interest is in the pieces, not the graph (which can be freely reorganized), unless one aspires to be a number theorist.