English

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 66-dimensional GKM manifolds with 44 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 CP3\mathbb{C} P^3 with standard complex structure (P2) blow up of S6S^6 at a fixed point, diffeomorphic to CP3\mathbb{C} P^3 (P3) CP3\mathbb{C} P^3 as the homogeneous space Sp(2)/(U(1)×Sp(1))\mathrm{Sp}(2)/(\mathrm{U}(1) \times \mathrm{Sp}(1)) with non-standard almost complex structure (Q1) complex quadric Q3Q_3 with standard complex structure (Q2) blow up of S6S^6 along isotropy 22-sphere, diffeomorphic to Q3Q_3 (S) S2×S4S^2 \times S^4, obtained as equivariant gluing along orbits of two S6S^6'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}
}
R2 v1 2026-07-01T10:40:54.773Z