Low-dimensional GKM theory

TL;DR

This survey explores recent advances in low-dimensional GKM theory, highlighting how the interplay between geometry and combinatorics enhances understanding of torus actions in equivariant topology.

Contribution

It provides a comprehensive overview of new results in low-dimensional GKM theory, emphasizing the interaction between geometry and combinatorics.

Findings

Enhanced understanding of low-dimensional GKM spaces

New combinatorial characterizations in low dimensions

Connections between geometry and combinatorics in torus actions

Abstract

GKM theory is a powerful tool in equivariant topology and geometry that can be used to generalize classical ideas from (quasi)toric manifolds to more general torus actions. After an introduction to the topic this survey focuses on recent results in low dimensions, where the interaction between geometry and combinatorics turns out to be particularly fruitful.