Almost complex circle actions with few fixed points

TL;DR

This paper investigates the existence of almost complex circle actions with a small number of fixed points, proving non-existence in certain dimensions and constructing examples in others.

Contribution

It proves the non-existence of such actions with three fixed points in dimension 8 and constructs infinite examples with two fixed points in dimension 6.

Findings

No almost complex circle actions with three fixed points in dimension 8.

Existence of an infinite series of 6-dimensional manifolds with two fixed points.

Provides new examples of almost complex circle actions in low dimensions.

Abstract

We show that almost complex circle actions with exactly three fixed points do not exist in dimension 8 and present an infinite series of 6-dimensional manifolds possessing an almost complex circle action with exactly two fixed points.