# Questions tagged [milnor-invariant]

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4
questions

**3**

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50 views

### On the milnor number of analytic germ map

If $f:(\mathbb{C}^n,0) \to (\mathbb{C},0)$ is an analytic germ with an isolated singularity, then the Milnor number of $f$, denoted by $\mu(f)$ can be defined as $\dim_{\mathbb{C}} \mathcal{O}_n/\text{...

**3**

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**1**answer

272 views

### Linking number a complete invariant of link homotopy

I read in Milnor's article "Link groups", where he defines invariants to classify links up to link homotopy, that the linking number is a complete invariant which can tell almost trivial two ...

**2**

votes

**2**answers

435 views

### Bounds for the milnor number of a hypersurface singularity

I am having a hard time in finding an upper bound in terms of the degree and the dimension for the Milnor number of an isolated hypersurface singularity. I am mostly interested in surfaces on the ...

**7**

votes

**1**answer

254 views

### A $k$-component link defines a map $T^{k}\rightarrow \mathrm{Conf}_{k} S^{3}$. Does the homotopy type capture Milnor's invariants?

A $k$-component link defines a map $T^{k}\rightarrow \mathrm{Conf}_{k} S^{3}$. Does the homotopy type of this map capture the Milnor invariants?
Some special cases:
$k=2$, no, it's null homologous, ...