On the bordism group for group actions on the torus

TL;DR

This paper investigates the bordism problem for group actions on the torus, providing examples of actions that cannot extend to bounding 3-manifolds, thus addressing a previously posed question.

Contribution

It introduces new examples of group actions on the torus that cannot be extended to bounding 3-manifolds, solving an open problem from prior research.

Findings

Examples of non-extendable group actions on the torus.

Resolution of a previously open question in the field.

Insights into the bordism properties of torus actions.

Abstract

In this short note, we study the bordism problem for group actions on the torus and give examples of groups acting on the torus by diffeomorphisms isotopic to the identity that cannot be extended to an action on a bounding 3-manifold. This solves a question raised in the previous work of the authors.