The big Dehn surgery graph and the link of S^3

TL;DR

This paper explores the structure and properties of the Big Dehn Surgery Graph, focusing on the link of S^3, and investigates its geometric and topological features along with subgraphs and open questions.

Contribution

It provides new insights into the geometry and topology of the Big Dehn Surgery Graph and examines its subgraphs and related open problems.

Findings

Characterization of the link of S^3 within the graph

Results on the geometric structure of the Big Dehn Surgery Graph

Identification of interesting subgraphs and posing of key questions

Abstract

In a talk at the Cornell Topology Festival in 2005, W. Thurston discussed a graph which we call "The Big Dehn Surgery Graph", B. Here we explore this graph, particularly the link of S^3, and prove facts about the geometry and topology of B. We also investigate some interesting subgraphs and pose what we believe are important questions about B.