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29 votes
2 answers
2k views

Contractibility of the space of Jordan curves

Is the space of Jordan curves in $\textbf{R}^2$ contractible? In other words, is there a canonical or continuous way to deform each Jordan curve to the unit circle $\textbf{S}^1$. If the curves are ...
Mohammad Ghomi's user avatar
3 votes
2 answers
459 views

Smooth paths on affine varieties

I have the following question which is in some way related to an application of Randell Isotopy Theorem to complex hyperplane arrangements. Let $h,k\geq1$ be integer numbers and let $F_{1},\ldots,F_{...
snaleimath's user avatar
3 votes
2 answers
517 views

Connected complement manifold

I'm working on some problem in algebraic geometry. I need a reference to the following result: Let $h\in\mathbb{N}$ with $h\geq1$ and let $F\in\mathbb{C}\left[x_{1},\ldots,x_{h}\right]$ be a non ...
snaleimath's user avatar