Six-dimensional GKM manifolds with four fixed points
Geometric Topology
2026-02-19 v1 Algebraic Topology
Combinatorics
Differential Geometry
Abstract
In this paper, we study -dimensional GKM manifolds with fixed points. We classify all possible GKM graphs, and for each type of graph we construct a manifold, proving the existence. We show that six types occur. (P1) complex projective space with standard complex structure (P2) blow up of at a fixed point, diffeomorphic to (P3) as the homogeneous space with non-standard almost complex structure (Q1) complex quadric with standard complex structure (Q2) blow up of along isotropy -sphere, diffeomorphic to (S) , obtained as equivariant gluing along orbits of two 's
Keywords
Cite
@article{arxiv.2602.16225,
title = {Six-dimensional GKM manifolds with four fixed points},
author = {Donghoon Jang and Shintaro Kuroki and Mikiya Masuda and Takashi Sato},
journal= {arXiv preprint arXiv:2602.16225},
year = {2026}
}