LECTURES ON ZARISKI VAN-KAMPEN THEOREM 1. Introduction ...
LECTURES ON ZARISKI VAN-KAMPEN THEOREM 1. Introduction ...
LECTURES ON ZARISKI VAN-KAMPEN THEOREM 1. Introduction ...
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<strong>LECTURES</strong> <strong>ON</strong> <strong>ZARISKI</strong> <strong>VAN</strong>-<strong>KAMPEN</strong> <strong>THEOREM</strong> 21<br />
Proof. Any lasso around an irreducible component of D is null-homotopic in M.<br />
Hence Σ(D i ) is contained in the kernel of ι ∗ .<br />
Suppose that a loop f : I → M \D with the base point b represents an element of<br />
Ker ι ∗ . Then f is null-homotopic in M, and hence there is a homotopy F : I × I →<br />
M from F |I ×{0} = f to F |I ×{1} =0 b that is stationary on the boundary<br />
∂I. Noting that dim Sing D
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