New York Journal of Mathematics
Volume 25 (2019), 315-327


Chi-Kwong Fok

Equivariant formality in K-theory

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Published: March 26, 2019.
Keywords: Equivariant K-theory, equivariant cohomology, equivariant formality, Lie group, group action.
Subject: 19L47; 55N15; 55N91.

In this note we present an analogue of equivariant formality in K-theory and show that it is equivalent to equivariant formality á la Goresky-Kottwitz-MacPherson. We also apply this analogue to give alternative proofs of equivariant formality of conjugation action on compact Lie groups, left translation action on generalized flag manifolds, and compact Lie group actions with maximal rank isotropy subgroups.


We would like to gratefully acknowledge the anonymous referee for the critical comments on the early drafts of this paper and especially the suggestions for improving Section 3.3. We would like to thank Ian Agol for answering a question related to the proof of Theorem 3.2.

Author information

Chi-Kwong Fok:
National Center for Theoretical Sciences
Mathematics Division
National Taiwan University
Taipei 10617, Taiwan, and
School of Mathematical Sciences
The University of Adelaide
Adelaide, SA 5005, Australia