A short introduction to shadows of 4-manifolds

TL;DR

This paper provides a comprehensive introduction to Turaev's shadows, a technique for studying 3- and 4-manifolds, summarizing recent developments without presenting new results.

Contribution

It offers a self-contained overview and practical guide to shadows theory, facilitating understanding and application in topology research.

Findings

Summarizes recent results on shadows in 3- and 4-manifold topology

Serves as an accessible introduction and reference for researchers

Highlights the utility of shadows as a tool in low-dimensional topology

Abstract

We give a self-contained introduction to the theory of Turaev's shadows as a tool to study 3 and 4-manifolds. The goal of the present paper twofold: on one side it is intended to be a shortcut to a basic use of the theory of shadows, on the other side it gives a sketchy overview of some of the recent results on shadows. No original result is proved here and most of the details of the proofs are not included.