Stratifiable maps and topological invariants
Stratifiable maps and topological invariants
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可分层地图和拓扑不变量
DOI：
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发表时间：
1991
期刊：
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通讯作者：
J. Shaneson
中科院分区：
文献类型：
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作者：
S. Cappell;J. Shaneson
设X和Y是空间，f：X-Y是它们之间的映射.然后，拓扑学（和几何学）中的一大类问题都涉及试图通过f将X和Y的不变量联系起来。这种尝试已经成功的情况下，X和Y流形和f的投影纤维丛，许多类型的重要不变量。例如，ChernHirzebruch-Serre [CHS]的结果断言，对于单连通的Y，X的签名是Y和纤维f 1（y）的签名的乘积。在本文中，我们进行的地图，其中纤维可能会有所不同，从点到点的研究。空间X和Y将是具有偶数余维层的任何惠特尼分层空间（例如，代数簇）和f将是分层映射。这实质上意味着，对于V是Y的一个层的分量（因此V是一个开流形），f 1V是X的一个层的并集，并且f到f 71 V的限制是一个局部平凡纤维丛。例如，子解析集的子解析映射可以分层，关于Whitney
Let X and Y be spaces and f: X -Y be a map between them. Then a large family of problems in topology (and geometry) involve the attempt to relate the invariants of X and Y via f. This attempt has been successful often for the case X and Y manifolds and f the projection of a fibre bundle, for many types of important invariants. For example, the result of ChernHirzebruch-Serre [CHS] asserts that for Y simply connected, the signature of X is the product of the signatures of Y and of the fibre f 1 (y) . In this paper we undertake the study of maps in which the fiber may vary from point to point. The spaces X and Y will be any Whitney stratified spaces with even codimension strata (e.g., algebraic varieties) and f will be a stratified map. This means essentially that for V a component of a stratum of Y (thus V is an open manifold), f 1V is a union of strata of X and the restriction of f to f71V is a locally trivial fibre bundle. For example, subanalytic maps of subanalytic sets can be stratified, with respect to Whitney