https://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture
first criticism: a circle is not equivalent to a point.
this reminds me of if IIMarckus was being pedantic about "mathematics has no concept of zoom."
To establish that the Poincaré sphere was different from the 3-sphere, Poincaré introduced a new topological invariant, the fundamental group, and showed that the Poincaré sphere had a fundamental group of order 120, while the 3-sphere had a trivial fundamental group. In this way he was able to conclude that these two spaces were, indeed, different.
1. what is the Poincare sphere
2. how dare you say a point is the same thing as a loop
first criticism: a circle is not equivalent to a point.
this reminds me of if IIMarckus was being pedantic about "mathematics has no concept of zoom."
To establish that the Poincaré sphere was different from the 3-sphere, Poincaré introduced a new topological invariant, the fundamental group, and showed that the Poincaré sphere had a fundamental group of order 120, while the 3-sphere had a trivial fundamental group. In this way he was able to conclude that these two spaces were, indeed, different.
1. what is the Poincare sphere
2. how dare you say a point is the same thing as a loop
