3 ms·
Nice presentation. I would probably have written it as an additive group (and then shown that the two strand braid was isomorphic with ℤ) as a further bidirect
by MarkusQ 11mo ago
Nice presentation. I would probably have written it as an additive group (and then shown that the two strand braid was isomorphic with ℤ) as a further bidirectional intuition anchor (both "look, this new thing relates to something you are familiar with" and "this thing you are familiar with generalizes in unexpected ways").
Definitely liked the exploration of how theorems arise from speculation, and don't spring fully formed straight from Zeus's forehead.
- geordiew 11mo agothe problem with additive notation is that the braid group isn't commutative when number of strands is > 2.
- MarkusQ 11mo agoExcellent point. I tend to enjoy "garden path" pedagogy, leading the students to surprising twists and having them explore -- but it's important to lead and not mislead. So yeah, multiplicative notation is probably better.