Six-dimensional GKM manifolds with four fixed points
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910025654468608 |
|---|---|
| author | Jang, Donghoon Kuroki, Shintaro Masuda, Mikiya Sato, Takashi |
| author_facet | Jang, Donghoon Kuroki, Shintaro Masuda, Mikiya Sato, Takashi |
| contents | In this paper, we study $6$-dimensional GKM manifolds with $4$ 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 $\mathbb{C} P^3$ with standard complex structure
(P2) blow up of $S^6$ at a fixed point, diffeomorphic to $\mathbb{C} P^3$
(P3) $\mathbb{C} P^3$ as the homogeneous space $\mathrm{Sp}(2)/(\mathrm{U}(1) \times \mathrm{Sp}(1))$ with non-standard almost complex structure
(Q1) complex quadric $Q_3$ with standard complex structure
(Q2) blow up of $S^6$ along isotropy $2$-sphere, diffeomorphic to $Q_3$
(S) $S^2 \times S^4$, obtained as equivariant gluing along orbits of two $S^6$'s |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Six-dimensional GKM manifolds with four fixed points Jang, Donghoon Kuroki, Shintaro Masuda, Mikiya Sato, Takashi Geometric Topology Algebraic Topology Combinatorics Differential Geometry In this paper, we study $6$-dimensional GKM manifolds with $4$ 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 $\mathbb{C} P^3$ with standard complex structure (P2) blow up of $S^6$ at a fixed point, diffeomorphic to $\mathbb{C} P^3$ (P3) $\mathbb{C} P^3$ as the homogeneous space $\mathrm{Sp}(2)/(\mathrm{U}(1) \times \mathrm{Sp}(1))$ with non-standard almost complex structure (Q1) complex quadric $Q_3$ with standard complex structure (Q2) blow up of $S^6$ along isotropy $2$-sphere, diffeomorphic to $Q_3$ (S) $S^2 \times S^4$, obtained as equivariant gluing along orbits of two $S^6$'s |
| title | Six-dimensional GKM manifolds with four fixed points |
| topic | Geometric Topology Algebraic Topology Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2602.16225 |