Non-principal T-duality, generalized complex geometry and blow-ups

TL;DR

This paper extends T-duality to manifolds with non-principal torus actions using elliptic tangent bundles, enabling the transport of generalized complex structures and providing new insights into classifying such actions.

Contribution

It introduces a framework for non-principal T-duality via elliptic tangent bundles, broadening the scope of T-duality in generalized complex geometry.

Findings

Established a method to transport generalized complex structures under non-principal T-duality.

Connected elliptic tangent bundles with the classification of torus actions.

Provided new tools for analyzing singularities in torus actions.

Abstract

We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the elliptic tangent bundle. Using this Lie algebroid, we explain how certain invariant generalized complex structures can be transported via T-duality. Along the way, we use the elliptic tangent bundle to define connections for these torus action, and give new insight to the classification of such actions by Haefliger-Salem.