Talk:Möbius energy

Definition

What is the definition of Möbius energy? 2607:8400:2802:10:250:56FF:FEAB:339C (talk) 20:14, 10 June 2015 (UTC)

Yes, this article has a big problem. Currently, the article doesn't define the mathematical concept about which it is about! Well observed. Mr. Barris (talk) 17:31, 15 July 2016 (UTC)

I am not an expert in this matter, but I see the definition in the article available on the site of Zhenghan Wang. There, click Research Interests -> Publications and slides -> (Items 2 and 3). Boris Tsirelson (talk) 19:16, 15 July 2016 (UTC)

By the way, the link to Möbius transformation could better link to Möbius transformation#Higher dimensions. Boris Tsirelson (talk) 19:24, 15 July 2016 (UTC)

Logical equivalence doesn't mean two things are the same

The article defines knots equivalence as follows:

"The idea of knot equivalence is to give a precise definition of when two knots should be considered the same even when positioned quite differently in space. A mathematical definition is that two knots $K_{1},K_{2}$ are equivalent if there is an orientation-preserving homeomorphism $h\colon \mathbb {R} ^{3}\to \mathbb {R} ^{3}$ with $h(K_{1})=K_{2}$, and this is known as an ambient isotopy."

This does happen to be logically equivalent to ambient isotopy, but it is not the same as ambient isotopy.

Isotopy requires a continuous family of embeddings. This doesn't mention any continuous family. It is a nontrivial theorem to show that these are logically equivalent. It is best not to confuse the reader with misstatements like this.50.205.142.35 (talk) 14:28, 7 December 2019 (UTC)

True. I'll correct that formulation. Boris Tsirelson (talk) 18:01, 7 December 2019 (UTC)