Equivariant cobordism for torus actions

被引:10
|
作者
Krishna, Amalendu [1 ]
机构
[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India
关键词
Algebraic cobordism; Group actions; ALGEBRAIC COBORDISM; ORIENTED COHOMOLOGY; SCHUBERT CALCULUS; HOMOLOGY;
D O I
10.1016/j.aim.2012.07.025
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the equivariant cobordism groups for the action of a split torus T on varieties over a field k of characteristic zero. We show that for T acting on a variety X. there is an isomorphism Omega(T)(*) (X) circle times(Omega)*(BT) L congruent to(->) Omega(*)(X). As applications, we show that for a connected linear algebraic group G acting on a k-variety X, the forgetful map Omega(G)(*)(X) -> Omega(*)(X) is surjective with rational coefficients. As a consequence, we describe the rational algebraic cobordism ring of algebraic groups and flag varieties. We prove a structure theorem for the equivariant cobordism of smooth projective varieties with torus action. Using this, we prove various localization theorems and a form of Bolt residue formula for such varieties. As an application, we show that the equivariant cobordism of a smooth variety X with torus action is generated by the invariant cobordism cycles in Omega(*)(X) as Omega*(BT)-module. (C) 2012 Elsevier Inc. All rights reserved.
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页码:2858 / 2891
页数:34
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