On Higher Homotopy Groups of Pencils
نویسنده
چکیده
We consider a large, convenient enough class of pencils on singular complex spaces. By introducing variation maps in homotopy, we prove in a synthetic manner a general Zariski-van Kampen type result for higher homotopy groups, which in homology is known as the “second Lefschetz theorem”.
منابع مشابه
Homotopy Variation Map and Higher Homotopy Groups of Pencils
We prove in a synthetic manner a general Zariski-van Kampen type theorem for higher homotopy groups of pencils on singular complex spaces.
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is bijective for j < n− 1 and surjective for j = n− 1. The kernel of the surjection in dimension n − 1 is described by the “second Lefschetz theorem”, whenever X0 is a generic member of a generic pencil, i.e. this pencil has only nondegenerate critical points. Loosely speaking, each critical point produces a vanishing cycle and those vanishing cycles together generate ker(Hj(X0,Z) → Hj(X,Z)). A...
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