*Published Paper*

**Inserted:** 6 apr 2004

**Last Updated:** 21 nov 2005

**Journal:** Mathematische Zeitschrift

**Volume:** 251

**Pages:** 535-549

**Year:** 2005

**Notes:**

DOI:10.1007*s00209-005-0820-y*

**Abstract:**

We show that maps from $B^n$ to a smooth compact boundaryless manifold ${\cal Y}$ which are smooth out of a singular set of dimension $n-2$ are dense for the strong topology in $W^{1/2}(B^n,{\cal Y})$. We also prove that for $n{\geq} 2$ smooth maps from $B^n$ to ${\cal Y}$ are dense in $W^{1/2}(B^n,{\cal Y})$ if and only if \,${\pi}_1({\cal Y})=0$, i.e. the first homotopy group of ${\cal Y}$ is trivial.

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