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Six-dimensional GKM manifolds with four fixed points
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Six-dimensional GKM manifolds with four fixed points
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Paper
Six-dimensional GKM manifolds with four fixed points
2026
Overview
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 \\(C P^3\\) with standard complex structure (P2) blow up of \\(S^6\\) at a fixed point, diffeomorphic to \\(C P^3\\) (P3) \\(C P^3\\) as the homogeneous space \\(Sp(2)/(U(1) 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 S^4\\), obtained as equivariant gluing along orbits of two \\(S^6\\)'s
Publisher
Cornell University Library, arXiv.org
Subject
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