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arXiv math/0011123math.AT
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因子的公共子丛与交

Common subbundles and intersections of divisors

N. P. Strickland

摘要:

设V_0和V_1是空间X上的复向量丛。我们使用形式群上的因子理论,给出了当V_0和V_1可以嵌入到丛U中,使得V_0 \cap V_1处处至少具有k维时,广义上同调中的障碍消失。我们研究各种代数普遍的例子与此相关的问题,并表明,它们产生于相应的拓扑普遍的例子的广义上同调。这扩展和重新解释早期的工作退化类普通上同调或相交理论。

英文摘要:

Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that V_0\cap V_1 has dimension at least k everywhere. We study various algebraic universal examples related to this question, and show that they arise from the generalised cohomology of corresponding topological universal examples. This extends and reinterprets earlier work on degeneracy classes in ordinary cohomology or intersection theory.

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