Chern numbers of manifolds with torus action

TL;DR

This paper demonstrates that any set of Chern numbers from an almost complex manifold of dimension at least six can be realized by a connected manifold with a torus action, linking topological invariants to symmetry actions.

Contribution

It establishes that all possible Chern number sets for high-dimensional almost complex manifolds can be realized with torus symmetries, expanding understanding of geometric structures.

Findings

Any Chern number set can be realized with a torus action

Connected almost complex manifolds can have prescribed Chern numbers

Torus actions can be incorporated into manifold constructions

Abstract

We show that every set of numbers that occurs as the set of Chern numbers of an almost complex manifold $M^{2n}$, $n\geqslant 3$, may be realized as the set of Chern numbers of a connected almost complex manifold with an almost complex action of two-dimensional compact torus.