1.1 Suppose X is a compact n-dimensional complex manifold. Each partition I = {i_1, i_2, …, i_r} of n corresponds to a Chern number c~I (X) = ε(c~(i1) (X) union c~(i2) (X) union … union c~(ir) (X) intersect [X]) ∈ H~(2k) (X; Z) are the Chern classes of the tangent bundle, [X] ∈ H_(2n) (X; Z) is the fundamental class, and ε:H_0(X; Z) → Z is the augmentation. Many invariants of X (such as its complex cobordism class) may be expressed in terms of its Chern numbers ([Mi], [St]). During the last 25 years, characteristic classes of singular spaces have been defined in a variety of contexts: Whitney classes of Euler spaces [Su], [H-T], [Ak], Todd classes of singular varieties [BFM], Chern classes of singular algebraic varieties [Mac], L-classes of stratified spaces with even codimension strata [GM1], Wu classes of singular spaces [Go2], [GP] (to name a few). However, these characteristic classes are invariably homology classes and as such, they cannot be multiplied with each other. In some cases it has been found possible to "lift" these classes from homology to intersection homology, where (some) characteristic numbers may be formed ([BBF], [BW], [Go2], [GP], [T]).
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机译：1.1假设X是一个紧凑的n维复流形。 n的每个分区I = {i_1，i_2，…，i_r}对应于Chern数c〜I（X）=ε（c〜（i1）（X）联合c〜（i2）（X）联合... union c 〜（ir）（X）相交[X]）∈H〜（2k）（X; Z）是切线束的Chern类，[X]∈H_（2n）（X; Z）是基类， ε：H_0（X; Z）→Z是扩充。 X的许多不变量（例如复杂的cobordism类）可以用其Chern数（[Mi]，[St]）表示。在最近的25年中，在各种情况下定义了奇异空间的特征类：欧拉空间的Whitney类[Su]，[HT]，[Ak]，奇异变体的Todd类[BFM]，Chern奇异类代数变体[Mac]，具有均匀维数层的分层空间的L类[GM1]，奇异空间的Wu类[Go2]，[GP]（仅举几例）。但是，这些特征类别始终是同源类别，因此它们不能彼此相乘。在某些情况下，已经发现可以将这些类从同源性“提升”到交集同源性，其中可以形成（一些）特征数（[BBF]，[BW]，[Go2]，[GP]，[T]） 。
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