Vladimir Turaev, friend and colleague

TL;DR

This paper reviews Vladimir Turaev's influential contributions to quantum topology, highlighting his innovative techniques in knot theory, 3-manifold invariants, and the development of quantum topology over the past 45 years.

Contribution

It provides a comprehensive overview of Turaev's pioneering work and its impact on low-dimensional topology and mathematical physics.

Findings

Turaev introduced new tools transforming knot and link invariants.

He helped establish quantum topology as a major research area.

His work connected topology with mathematical physics.

Abstract

This is a biography and a report on the work of Vladimir Turaev. Using fundamental techniques that are rooted in classical topology, Turaev introduced new ideas and tools that transformed the field of knots and links and invariants of 3-manifolds. He is one of the main founders of the new topic called quantum topology. In surveying Turaev's work, this article will give at the same time an overview of an important part of the intense activity in low-dimensional topology that took place over the last 45 years, with its connections with mathematical physics.