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Wagner’s Theory of Generalised Heaps

  • Book
  • © 2017

Overview

Authors:
  1. Christopher D. Hollings

    1. Mathematical Institute, University of Oxford, Oxford, United Kingdom

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  2. Mark V. Lawson

    1. Department of Mathematics, Heriot-Watt University, Edinburgh, United Kingdom

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  • Presents original discussion, insight and contextual development of Wagner’s work

  • Illuminates modern relevance through applications to current mathematical research

  • Serves as a reference for Wagner's theory of generalised heaps

  • Contains a technical discussion of the translation: notation, how and why technical words have been translated

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Christopher D. Hollings, Mark V. Lawson
    Pages 1-3

  3. Viktor Vladimirovich Wagner (1908–1981)

    • Christopher D. Hollings, Mark V. Lawson
    Pages 5-6

  4. Wagner’s Work in Historical Context

    • Christopher D. Hollings, Mark V. Lawson
    Pages 7-23

  5. Notes on the Translations

    • Christopher D. Hollings, Mark V. Lawson
    Pages 25-29

  6. A Ternary Algebraic Operation in the Theory of Coordinate Structures

    • Christopher D. Hollings, Mark V. Lawson
    Pages 31-35

  7. On the Theory of Partial Transformations

    • Christopher D. Hollings, Mark V. Lawson
    Pages 37-41

  8. Generalised Groups

    • Christopher D. Hollings, Mark V. Lawson
    Pages 43-47

  9. Theory of Generalised Heaps and Generalised Groups

    • Christopher D. Hollings, Mark V. Lawson
    Pages 49-145

  10. Generalised Heaps as Affine Structures

    • Christopher D. Hollings, Mark V. Lawson
    Pages 147-169

  11. Back Matter

    Pages 171-189
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Keywords

About this book

The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts.  This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research.  Along with a translation of Wagner’s main work in this area,  his 1953 paper ‘Theory of generalised heaps and generalised groups,’ the book also includes translations of three short precursor articles that provide additional context for his major work.

Researchers and students interested in both algebra (in particular, heaps, semiheaps, generalised heaps, semigroups, and groups) and differential geometry will benefit from the techniques offered by these translations, owing to the natural connections between generalised heaps and generalised groups, and the role played by these concepts in differential geometry.  This book gives examples from present-day mathematics where ideas related to Wagner’s have found fruitful applications.

Reviews

“This book will be invaluable to whoever is interested in the algebraic structures afforded by the description of global objects through local charts, the history of the surrounding ideas, and the sources. Justifying its title, it focusses on Wagner's contributions to the theory of heaps and their generalisations … . As a consequence, even readers who are not interested primarily in Wagner or heaps will find rewards for their time spent with this book.” (Markus Szymik, Mathematical Reviews, July, 2018)

“This book presents the in the West little-known work of the Russian differential geometer Wagner … . the book is easy to read and should be of interest to mathematicians and PhD students interested in differential geometry and contemporary theories of physics.” (Jaak Henno, zbMATH 1403.20001, 2019)

Authors and Affiliations

  • Mathematical Institute, University of Oxford, Oxford, United Kingdom

    Christopher D. Hollings

  • Department of Mathematics, Heriot-Watt University, Edinburgh, United Kingdom

    Mark V. Lawson

Bibliographic Information

  • Book Title: Wagner’s Theory of Generalised Heaps

  • Authors: Christopher D. Hollings, Mark V. Lawson

  • DOI: https://doi.org/10.1007/978-3-319-63621-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018 2017

  • Hardcover ISBN: 978-3-319-63620-7Published: 18 September 2017

  • Softcover ISBN: 978-3-319-87597-2Published: 11 August 2018

  • eBook ISBN: 978-3-319-63621-4Published: 09 September 2017

  • Edition Number: 1

  • Number of Pages: XV, 189

  • Number of Illustrations: 19 b/w illustrations

  • Topics: Group Theory and Generalizations, History of Mathematical Sciences, Differential Geometry

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