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Topology and Geometry
IRMA Lectures in Mathematics and Theoretical Physics Vol. 33

Topology and Geometry

A Collection of Essays Dedicated to Vladimir G. Turaev

Editor:
Athanase Papadopoulos (Université de Strasbourg and CNRS, France)


ISBN print 978-3-98547-001-3, ISBN online 978-3-98547-501-8
DOI 10.4171/IRMA/33
July 2021, 698 pages, hardcover, 16.5 x 23.5 cm.
99.00 Euro

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.

Keywords: higher linking numbers for links in the 3-sphere, intersection of loops on surfaces, Turaev cobracket, Poincaré complexes, Poincaré duality, spin structures in 3-manifolds, explicit constructions of cocycles, Turaev surface, Turaev volume, skein module, quantum invariants of knots, links and 3-manifolds, 6j-symbols; Turaev–Viro invariant, Reshetikhin–Turaev invariant, TQFT, HQFT, Gauss words and links, enumeration problems in topology and group theory, generalizations of the Thurston norm, knotoids, knots, links, braids, intersections and self-intersections of loops on surfaces, cobrackets, combinatorial group theory, metric geometry, phylogenetics

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