Orientability and equivariant oriented cobordism of 2-torus manifolds

TL;DR

This paper establishes a comprehensive criterion for orientability of 2-torus manifolds with fixed points, extends previous results, and explores their equivariant cobordism classes, contributing to the understanding of their topological and geometric properties.

Contribution

It provides a necessary and sufficient condition for orientability and investigates the equivariant oriented cobordism classes of locally standard 2-torus manifolds.

Findings

Derived a criterion for orientability of 2-torus manifolds

Constructed manifolds with boundary related to 2-torus manifolds

Analyzed equivariant oriented cobordism classes

Abstract

We give a necessary and sufficient condition for the orientability of a locally standard 2-torus manifold with a fixed point which generalizes previous results of Nakayama-Nishimura in 2005 and Soprunova-Sottile in 2013. We construct manifolds with boundary where the boundary is a disjoint union of locally standard 2-torus manifolds. We discuss equivariant oriented cobordism class of locally standard 2-torus manifolds.