Equivariant cohomology of odd-dimensional complex quadrics from a combinatorial point of view

Abstract

This paper aims to determine the ring structure of the torus equivariant cohomology of odd-dimensional complex quadrics by computing the graph equivariant cohomology of their corresponding GKM graphs. We show that its graph equivariant cohomology is generated by three types of subgraphs in the GKM graph, which are subject to five different types of relations. Furthermore, we consider the relationship between the two graph equivariant cohomology rings induced by odd- and even-dimensional complex quadrics.

arXiv commentIn this version, we correct an error in the presentation of the graph equivariant cohomology ring and several related gaps in the proofs that appeared in the published version of our paper [Internat. J. Math. 37(3), Paper No. 2650021, 36 pp., 2026]. We sincerely thank Prof. Suyoung Choi for pointing out a mistake in an earlier version of the manuscript and for his helpful comments