The equivariant cohomology ring of regular varieties
The equivariant cohomology ring of regular varieties
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DOI：
10.1307/mmj/1080837743
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发表时间：
2002-11
影响因子：
0.9
通讯作者：
M. Brion;J. Carrell
中科院分区：
文献类型：
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作者：
M. Brion;J. Carrell
o ∈XT，因为X是T-稳定的。此外，X由[7]的引理1有限。因此，我们可以写X = {1 = o，2，. . .，r}。(3)显然，r = χ（X），X的欧拉特征线。设H ∈ T（X）表示X的复系数T-等变上同调环。为了定义它，设E是一个具有自由作用T的可压缩空间，且设XT =（X × E）/T（对角T作用的商）。则H T（X）= H（XT）。众所周知，点的等变上同调环H <$T（pt）是多项式环C[z]，其中z表示T的李代数上的线性形式
o ∈XT, since X is T-stable. Moreover, X is finite by Lemma 1 of [7]. Thus we may write X = {ζ1 = o, ζ2, . . . , ζr}. (3) Clearly r = χ(X), the Euler characteristic of X. Let H ∗ T(X) denote the T-equivariant cohomology ring of X with complex coefficients. To define it, let E be a contractible space with a free action of T and let XT = (X × E )/T (quotient by the diagonal T-action). Then H ∗ T(X) = H ∗(XT). It is well known that the equivariant cohomology ring H ∗ T(pt) of a point is the polynomial ring C[z], where z denotes the linear form on the Lie algebra of T