by Sóstenes Lins (Universidade Federal de Pernambuco, Brazil)

This book is about dealing with 3-manifolds using computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.

• Introduction
• Graph-Encoded Manifolds
• Elements of the Theory of 3-Gems
• Decomposition Theory: Handles
• Simplifying Dynamics: The TS^u_p-Algorithm
• The Generation and Classification of 3-Manifolds
• Getting Linking Numbers of 3-Manifolds
• Computing the Quantum Invariants from Blinks
• Appendices