Topology and Geometry

The present volume consists of a collection of essays dedicated to Vladimir Turaev.

The essays cover the large spectrum of topics in which Turaev has been interested, including knot and link invariants, quantum representations, TQFTs, state sum constructions, geometric structures on knot complements, Kleinian groups, geometric group theory and its relationship with 3-manifolds, mapping class groups, operads, mathematical physics, Grothendieck’s program, the philosophy of mathematics, and several other topics.

At the same time, this volume will give an overview of topics that are at the forefront of current research in topology and geometry. Some of the essays are research articles and contain new results, sometimes answering questions that were raised by Turaev. The rest of the essays are surveys that will introduce the reader to some key ideas in the field.