Smooth classification of locally standard $T^k$-manifolds

TL;DR

This paper classifies locally standard $T^k$-manifolds with a continuous section to the orbit map, providing a comprehensive understanding of their structure up to equivariant diffeomorphism.

Contribution

It introduces a classification framework for certain $T^k$-manifolds with a continuous section, expanding the understanding of their equivariant diffeomorphism types.

Findings

Classification of $T^k$-manifolds with a continuous section

Conditions for equivariant diffeomorphism classification

Structural insights into locally standard $T^k$-manifolds

Abstract

We study locally standard $T^k$-manifolds $M$. In particular, we study the case where there is a continuous section to the orbit map $\pi : M \rightarrow M/T$. We give a classification of $T^k$-manifolds satisfying these conditions up to equivariant diffeomorphism.