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196 are transverse to $Y$ or splittable along $Y$. |
196 are transverse to $Y$ or splittable along $Y$. |
197 \item Splittings. |
197 \item Splittings. |
198 Let $c\in \cC_k(X)$ and let $Y\sub X$ be a codimension 1 properly embedded submanifold of $X$. |
198 Let $c\in \cC_k(X)$ and let $Y\sub X$ be a codimension 1 properly embedded submanifold of $X$. |
199 Then for most small perturbations of $Y$ (e.g.\ for an open dense |
199 Then for most small perturbations of $Y$ (e.g.\ for an open dense |
200 subset of such perturbations, or for all perturbations satisfying |
200 subset of such perturbations, or for all perturbations satisfying |
201 a transversality condition) $c$ splits along $Y$. |
201 a transversality condition, c.f. Axiom \ref{axiom:splittings} much later) $c$ splits along $Y$. |
202 (In Example \ref{ex:maps-to-a-space(fields)}, $c$ splits along all such $Y$. |
202 (In Example \ref{ex:maps-to-a-space(fields)}, $c$ splits along all such $Y$. |
203 In Example \ref{ex:traditional-n-categories(fields)}, $c$ splits along $Y$ so long as $Y$ |
203 In Example \ref{ex:traditional-n-categories(fields)}, $c$ splits along $Y$ so long as $Y$ |
204 is in general position with respect to the cell decomposition |
204 is in general position with respect to the cell decomposition |
205 associated to $c$.) |
205 associated to $c$.) |
206 \item Product fields. |
206 \item Product fields. |