Circle actions on 8-dimensional almost complex manifolds with 4 fixed points

Abstract

Consider a circle action on an 8-dimensional compact almost complex manifold with 4 fixed points. To the author's knowledge, $S^2\times S^6$ is the only known example of such a manifold. In this paper, we prove that if the circle acts on an 8-dimensional compact almost complex manifold $M$ with 4 fixed points, all the Chern numbers and the Hirzebruch ${\chi }_y$-genus of $M$ agree with those of $S^2\times S^6$. In particular, $M$ is unitary cobordant to $S^2\times S^6$.

References in corpus (6)

• Symplectic periodic flows with exactly three equilibrium points
• The rigidity of Dolbeault-type operators and symplectic circle actions
• Circle actions on almost complex manifolds with isolated fixed points
• Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets
• Circle actions on almost complex manifolds with 4 fixed points
• Symplectic circle actions with isolated fixed points

Cited by in corpus (3)

• GKM manifolds are not rigid
• On circle actions with exactly three fixed points
• Circle actions on 6-dimensional oriented manifolds with 4 fixed points