2013年2月6日 · An isotopy is a deformation that involves only bending. It must be one-to-one and onto at every step. It must be one-to-one and onto at every step. In this way, any two …

$\begingroup$ Be aware that often when people say "isotopy" they mean "ambient isotopy," and ambient isotopy does give a homeomorphism like the one you ask for. $\endgroup$ – Cheerful …

2015年6月4日 · Now this is precisely the hypothesis we need to use the isotopy extension theorem: so any (locally flat/smooth) isotopy of embeddings automatically lifts to an ambient …

2018年1月6日 · Prove that the isotopy generated by a time-dependent symplectic vector field is a symplectomorphism Hot Network Questions Is it possible to perform a statistical analysis with …

2020年12月10日 · Equivalence of unoriented knots by ambient isotopy. 8. Difference between homotopy equivalence and ...

2018年6月14日 · I believe it's because curves with rational slope can be seen on the unit square with opposite sides identified (a typical way of realizing the torus) to be precisely the simple …

The key reference on regular isotopy seems to be the following paper: Kauffman, Louis H. “An invariant of regular isotopy.” Transactions of the American Mathematical Society 318, no. 2 …

2022年1月11日 · This is shown in most introductory topology books. For ambient isotopy we need to ensure properties (1) and (2) also hold for each transformation between our two equivalent …

Looking at the proof, Hirsch does not seem to take the precautions he took in Theorem 1.3 to avoid getting an 'isotopy' that moves the boundary to the interior of the manifold.

2015年6月23日 · Use ambient isotopy, as mentioned by the OP. Although the animation above shows an isotopy of embeddings of a circle into $\mathbb{R}^3$, this doesn't extend to an …