On Transition Functions of Topological Toric Manifolds

TL;DR

This paper demonstrates that topological toric manifolds can be covered by charts with transition functions as Laurent monomials, and characterizes certain toric manifolds via these functions up to equivariant diffeomorphism.

Contribution

It establishes a new description of topological toric manifolds using Laurent monomial transition functions and classifies some toric manifolds through these functions.

Findings

Transition functions are Laurent monomials of $z_j$ and $ar{z}_j$.

Topological toric manifolds can be described by these transition functions.

Certain toric manifolds are characterized up to equivariant diffeomorphism.

Abstract

We show that any topological toric manifold can be covered by finitely many open charts so that all the transition functions between these charts are Laurent monomials of $z_j$'s and $\bar{z}_j$'s. In addition, we will describe toric manifolds and some special class of topological toric manifolds in terms of transition functions of charts up to (weakly) equivariant diffeomorphism.