On the equivalence of integral T ^k-cohomology Chern numbers and T ^k-K-theoretic Chern numbers

Abstract

This paper mainly deals with the question of equivalence between equivariant cohomology Chern numbers and equivariant K-theoretic Chern numbers when the transformation group is a torus. By using the equivariant Riemann-Roch relation of Atiyah-Hirzebruch type, it is proved that the vanishing of equivariant cohomology Chern numbers is equivalent to the vanishing of equivariant K-theoretic Chern numbers.

Keywords

Equivariant K-theoretic Chern number / Equivariant cohomology Chern number / Equivariant bordism

References

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