Vladimir Turaev Books

Torsions of 3 dimensional Manifolds
Torsions of 3 dimensional Manifolds

By Vladimir Turaev

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The book is concerned with one of the most interesting and important topological invariants of 3-dimensional manifolds based on an original idea of Kurt Reidemeister (1935). This invariant, called...

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Introduction to Combinatorial Torsions
Introduction to Combinatorial Torsions

By Vladimir Turaev

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This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundati...

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If you’ve ever purchased a product online or in a store, you’ve likely come across a barcode. Behind these barcodes lies a standardized system that makes modern commerce possible. Two key codes often encountered are the EAN (European Article Number) and ISBN (International Standard Book Number). But what are they, how are they connected, and why are they so crucial? Let’s explore.

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