# zbMATH — the first resource for mathematics

On the homotopy of stratified spaces. (Sur l’homotopie des espaces stratifiés.) (French) Zbl 0940.55011
The author proves theorems concerning relative connectivity of complement of analytic subspaces. Let us mention theorems 3 and 4.
Theorem 3: Let $$M$$ be an $$n$$-dimensional real analytic manifold and $$Y$$ be $$d$$-dimensional closed analytic subspace, then $$(M,M\smallsetminus Y)$$ is $$(n-1-d)$$-connected.
Theorem 4: Let $$M$$ be a real compact analytic manifold of dimension $$n$$, and $$X$$ and $$Y$$ closed analytic subspaces. Suppose that $$X$$ and $$Y$$ admit analytic Whitney stratifications $$S$$ and $$S'$$ and that the strata of $$S$$ and $$S'$$ intersect transversely, then $$(X,X\smallsetminus (X\cap Y))$$ is $$(n- 1-d)$$-connected, with $$d$$ the dimension of $$Y$$.

##### MSC:
 55P15 Classification of homotopy type 57N80 Stratifications in topological manifolds 55Q52 Homotopy groups of special spaces
Full Text: