标题： 伪流形的等变L类 显示英文标题

标题： The Equivariant L-Class of Pseudomanifolds

摘要： 我们为一个紧李群在满足Witt条件的Whitney分层紧定向伪流形上的保持方向的作用构造了一个等变L类，例如在紧纯维复代数簇上。 该类位于等变有理同调中，其限制到平凡群时是Goresky-MacPherson L类。 对于流形上的光滑作用，该类与切丛的Borel同伦商的Hirzebruch L类等变Poincaré对偶。 我们在等变Künneth同构下提供了乘积公式。 如果群自由作用，则等变L类与轨道空间的Goresky-MacPherson L类相一致。 该构造方法基于建立Borel构造的有限维紧伪流形近似值的Whitney (B)正则性，以及作者针对Goresky-MacPherson L类的Verdier-Riemann-Roch型公式。 显示英文摘要

摘要： We construct an equivariant L-class for orientation preserving actions of a compact Lie group on a Whitney stratified compact oriented pseudomanifold that satisfies the Witt condition, for example on a compact pure-dimensional complex algebraic variety. The class lies in equivariant rational homology and its restriction to the trivial group is the Goresky-MacPherson L-class. For a smooth action on a manifold, the class is equivariantly Poincar\'e dual to the Hirzebruch L-class of the Borel homotopy quotient of the tangent bundle. We also provide a product formula under the equivariant K\"unneth isomorphism. If the group acts freely, then the equivariant L-class identifies with the Goresky-MacPherson L-class of the orbit space. The construction method rests on establishing Whitney (B)-regularity for finite-dimensional compact pseudomanifold approximations to the Borel construction, and on the author's Verdier-Riemann-Roch type formulae for the Goresky-MacPherson L-class.