# Tangent cones and $C^1$ regularity of definable sets

Date(s) : 30/06/2016   iCal
14 h 00 min - 15 h 00 min

In this talk we will present some criteria of tangent cones so that a definable set is a $C^1$ manifold. Namely, let $X$ be a connected locally closed definable set in $R^n$, we show that the following statements are equivalent
1) $X$ is a $C^1$ manifold
2) Tangent cone and paratangent cone of $X$ coincide,
3) The tangent cone $T_x X$ of $X$ at the point $x$ is k-dimensional linear subspace of $R^n$ (k does not depend on $x$) varies continuously in $x$, and the density $\theta(X, x) < 3/2$.

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