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Results tagged with differential-topology
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user 126243
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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Implicit function theorem and its consequence
Let $f:{\Bbb C}^{n+1}\to {\Bbb C}^n$ be a map defined by homogeneous polynomials. There is a point $p\in f^{-1}(0)$ and a neighbourhood $U$ of $p$ in $f^{-1}(0)$, such that $d(f)$ has rank $n$ at ever …
- 585
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Thom's first isotopy lemma
Thom's first isotopy lemma says that given $f:M\to P$ a smooth map between smooth manifolds and a closed Whitney stratified subset $S$ of $M$, such that
$f|_S:S\to P$ is proper and $f|_X:X\to P$ is a …
- 585
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‘Sur les groupes de tresses’ by Egbert Brieskorn
I have a very specific question. How does one check the following map
${\mathbb C}^n-\bigcup_{i\neq j} \{z \mid z_i= \pm z_j\}\to {({\mathbb C}^*)}^{n-1}-\bigcup_{i\neq j}\{w \mid w_i= w_j\}$ defined …
- 585