3 ms·
You can drop “seemingly”: SO(3) is indeed tree-dimensional. And SO(3) a.k.a. P^3 has fundamental group Z_2 a.k.a. GF(2), whereas T^3 has fundamental group Z^3,
by hanche 5y ago
You can drop “seemingly”: SO(3) is indeed tree-dimensional. And SO(3) a.k.a. P^3 has fundamental group Z_2 a.k.a. GF(2), whereas T^3 has fundamental group Z^3, so they are quite different beasts indeed.
- anon_tor_12345 5y agoyea you're right. kudos for explaining it so succinctly.