On Cappell-Shaneson’s homology $L$-classes of singular algebraic varieties
On Cappell-Shaneson’s homology $L$-classes of singular algebraic varieties
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奇异代数簇的 Cappell-Shaneson 同源 $L$ 类
DOI：
10.1090/s0002-9947-1995-1283567-6
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发表时间：
1995
影响因子：
1.3
通讯作者：
Shoji Yokura
中科院分区：
文献类型：
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作者：
Shoji Yokura
S. Cappell和J. Shaneson（分层映射和拓扑不变量），J. Amer。数学。Soc. 4(1991), 521-551)最近发展了同源l类理论，扩展了Goresky-MacPherson的同源l类理论。在本文中，我们证明了紧复，可能是奇异的代数变体的Cappell-Shaneson的同调l-类可以解释为一个从协变协协函数Q到满足一定规整条件的Q-同调函子H （； Q）的唯一自然变换，就像MacPherson的Chern类和Baum-Fulton-MacPherson的Todd类一样。
S. Cappell and J. Shaneson (Stratifiable maps and topological invariants, J. Amer. Math. Soc. 4 (1991), 521-551) have recently developed a theory of homology L-classes, extending Goresky-MacPherson's homology Lclasses. In this paper we show that Cappell-Shaneson's homology L-classes for compact complex, possibly singular, algebraic varieties can be interpreted as a unique natural transformation from a covariant cobordism function Q to the Q-homology functor H ( ; Q) satisfying a certain normalization condition, just like MacPherson's Chern classes and Baum-Fulton-MacPherson's Todd classes.