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Assume that $X$ is the complement of a plane algebraic curve $C$ in $\mathbb{C}^2$ and Y is the complement of the union of $C$ and a line $L$ (not contained in $C$). Assume that $Y$ is $K(\pi, 1)$. Is it true that $X$ is $K(\pi, 1)$? Why or why not?
Assume that $X$ is the complement of a plane algebraic curve $C$ and Y is the complement of the union of $C$ and a line $L$ (not contained in $C$). Assume that $Y$ is $K(\pi, 1)$. Is it true that $X$ is $K(\pi, 1)$? Why or why not?
Assume that $X$ is the complement of a plane algebraic curve $C$ in $\mathbb{C}^2$ and Y is the complement of the union of $C$ and a line $L$ (not contained in $C$). Assume that $Y$ is $K(\pi, 1)$. Is it true that $X$ is $K(\pi, 1)$? Why or why not?
Homotopy type of complement of a plane algebraic curves.
Assume that $X$ is the complement of a plane algebraic curve $C$ and Y is the complement of the union of $C$ and a line $L$ (not contained in $C$). Assume that $Y$ is $K(\pi, 1)$. Is it true that $X$ is $K(\pi, 1)$? Why or why not?
