On free $Z_p$-torus actions in dimension two and three

TL;DR

This paper proves the Halperin-Carlsson Conjecture for specific free torus actions on 2-dimensional CW-complexes and 3-manifolds, advancing understanding in algebraic topology.

Contribution

It confirms the conjecture for free $Z_p$-torus actions on 2D complexes and free $Z_2$-torus actions on 3-manifolds, providing new results in topological transformation groups.

Findings

Confirmed the conjecture for free $Z_p$-torus actions on 2D CW-complexes

Confirmed the conjecture for free $Z_2$-torus actions on 3-manifolds

Extended the validity of the conjecture in low-dimensional topology

Abstract

We confirm the Halperin-Carlsson Conjecture for free $Z_p$-torus actions (p is a prime) on 2-dimensional finite CW-complexes and free $Z_2$-torus actions on compact 3-manifolds.