Equivariant cobordism for torus actions

Krishna, Amalendu (2012) Equivariant cobordism for torus actions Advances in Mathematics, 231 (5). pp. 2858-2891. ISSN 0001-8708

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.aim.2012.07.025


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 ΩT*(X)⊗Ω*(BT) L → Ω*(X) source. As applications, we show that for a connected linear algebraic group G acting on a k-variety X, the forgetful map ΩG*(X) → Ω*(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 Bott 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 Ω*(X) as Ω(BT)-module.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Algebraic Cobordism; Group Actions
ID Code:102476
Deposited On:09 Mar 2018 10:47
Last Modified:09 Mar 2018 10:47

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