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Proceedings of ASARC Workshop Daecheon & Muju 2009
(2009 / vol.11 / no.2)
Introduction to GKM theory
Shintar^o KUROKI
Pages. 113-129   



GKM theory has been developed to compute torus equivariant cohomologies on some nice space called GKM space.
A set of GKM spaces consists of many classes in the spaces with torus actions, e.g., the torus manifold is the GKM space.
So we can expect that to study GKM spaces will lead us in a deep understanding of torus actions.
The aim of this article is to introduce GKM theory.



1. Introduction
2. Basics of equivariant cohomology
3. GKM manifold and its equivariant cohomology
4. GKM graph and graph equivariant cohomology
5. Relations with toric geometry
6. Problem