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Papers on Topology: Analysis Situs and Its Five Supplements

Translated by John Stillwell
A co-publication of the AMS and London Mathematical Society
Available Formats:
Softcover ISBN: 978-0-8218-5234-7
Product Code: HMATH/37
List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $52.80 Electronic ISBN: 978-1-4704-1840-3 Product Code: HMATH/37.E List Price:$62.00
MAA Member Price: $55.80 AMS Member Price:$49.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $99.00 MAA Member Price:$89.10
AMS Member Price: $79.20 Click above image for expanded view Papers on Topology: Analysis Situs and Its Five Supplements Translated by John Stillwell A co-publication of the AMS and London Mathematical Society Available Formats:  Softcover ISBN: 978-0-8218-5234-7 Product Code: HMATH/37  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$52.80
 Electronic ISBN: 978-1-4704-1840-3 Product Code: HMATH/37.E
 List Price: $62.00 MAA Member Price:$55.80 AMS Member Price: $49.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$99.00 MAA Member Price: $89.10 AMS Member Price:$79.20
• Book Details

History of Mathematics
History of Mathematics Source Series
Volume: 372010; 228 pp
MSC: Primary 01; 55; 57;
John Stillwell was the recipient of the Chauvenet Prize for Mathematical Exposition in 2005.

These famous papers, with their characteristic mixture of deep insight and inevitable confusion, are here presented complete and in English for the first time, with a commentary by their translator, John Stillwell, that guides the reader into the heart of the subject. One of the finest works of one of the great mathematicians is now available anew for students and experts alike.

Jeremy Gray

The AMS and John Stillwell have made an important contribution to the mathematics literature in this translation of Poincaré. For many of us, these great papers on the foundations of topology are given greater clarity in English. Moreover, reading Poincaré here illustrates the ultimate in research by successive approximations (akin to my own way of mathematical thinking).

Stephen Smale

I am a proud owner of the original complete works in green leather in French bought for a princely sum in Paris around 1975. I have read them extensively, and often during topology lectures I refer to parts of these works. I am happy that there is now the option for my students to read them in English.

Dennis Sullivan

The papers in this book chronicle Henri Poincaré's journey in algebraic topology between 1892 and 1904, from his discovery of the fundamental group to his formulation of the Poincaré conjecture. For the first time in English translation, one can follow every step (and occasional stumble) along the way, with the help of translator John Stillwell's introduction and editorial comments.

Now that the Poincaré conjecture has finally been proved, by Grigory Perelman, it seems timely to collect the papers that form the background to this famous conjecture. Poincaré's papers are in fact the first draft of algebraic topology, introducing its main subject matter (manifolds) and basic concepts (homotopy and homology). All mathematicians interested in topology and its history will enjoy this book.

This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, “Sources”, are classical mathematical works that served as cornerstones for modern mathematical thought.

Readership

Undergraduates, graduate students, and research mathematicians interested in topology and the history of topology.

• Table of Contents

• Chapters
• On Analysis Situs
• Analysis Situs
• Supplement to Analysis Situs
• Second supplement to Analysis Situs
• On certain algebraic surfaces: Third supplement to Analysis Situs
• Cycles on algebraic surfaces: Fourth supplement to Analysis Situs
• Fifth supplement to Analysis Situs
• Additional Material

• Reviews

• The current book provides a skillful translation of his [Poincaré's] breakthrough work in algebraic topology. . . . John Stillwell has done a marvelous job with his translations and editing. . . . Poincaré's prose flows smoothly - he was a pretty good writer, after all - and it is a delight to read. . . . I found this a charming contrast to the impersonality of many modern texts.

Bill Satzer, MAA Reviews
• The English translation of Poincaré's celebrated work Analysis situs, together with the series of "Compliments” he added between 1895 and 1904, makes available a remarkable resource to the non-francophone community. Darboux wrote of Poincaré that "when he drafted a memoir, he drafted it in one go, limiting himself to some crossings out, without coming back to what he had written”. Stillwell's translation admits us to this pouring forth of Poincaré's ideas, and to their consequences as played out in the supplements. Not only do we get a glimpse of Poincaré at work, but these papers contain the beginnings of the modern notions used in topology today and the connections they make with the ideas of the nineteenth century.

Analysis situs and its supplements have earned their place as the source of many rich ideas that developed into the field of algebraic topology. At the end of the introduction to Analysis situs Poincaré writes, "I do not think then that I have engaged in useless work in writing the present memoir”. The reader more than a century later will find that he or she will not engage in useless work in reading Poincaré's papers. We have Stillwell to thank for making such work easier with his translation.

John McCleary, Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
History of Mathematics Source Series
Volume: 372010; 228 pp
MSC: Primary 01; 55; 57;
John Stillwell was the recipient of the Chauvenet Prize for Mathematical Exposition in 2005.

These famous papers, with their characteristic mixture of deep insight and inevitable confusion, are here presented complete and in English for the first time, with a commentary by their translator, John Stillwell, that guides the reader into the heart of the subject. One of the finest works of one of the great mathematicians is now available anew for students and experts alike.

Jeremy Gray

The AMS and John Stillwell have made an important contribution to the mathematics literature in this translation of Poincaré. For many of us, these great papers on the foundations of topology are given greater clarity in English. Moreover, reading Poincaré here illustrates the ultimate in research by successive approximations (akin to my own way of mathematical thinking).

Stephen Smale

I am a proud owner of the original complete works in green leather in French bought for a princely sum in Paris around 1975. I have read them extensively, and often during topology lectures I refer to parts of these works. I am happy that there is now the option for my students to read them in English.

Dennis Sullivan

The papers in this book chronicle Henri Poincaré's journey in algebraic topology between 1892 and 1904, from his discovery of the fundamental group to his formulation of the Poincaré conjecture. For the first time in English translation, one can follow every step (and occasional stumble) along the way, with the help of translator John Stillwell's introduction and editorial comments.

Now that the Poincaré conjecture has finally been proved, by Grigory Perelman, it seems timely to collect the papers that form the background to this famous conjecture. Poincaré's papers are in fact the first draft of algebraic topology, introducing its main subject matter (manifolds) and basic concepts (homotopy and homology). All mathematicians interested in topology and its history will enjoy this book.

This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, “Sources”, are classical mathematical works that served as cornerstones for modern mathematical thought.

Readership

Undergraduates, graduate students, and research mathematicians interested in topology and the history of topology.

• Chapters
• On Analysis Situs
• Analysis Situs
• Supplement to Analysis Situs
• Second supplement to Analysis Situs
• On certain algebraic surfaces: Third supplement to Analysis Situs
• Cycles on algebraic surfaces: Fourth supplement to Analysis Situs
• Fifth supplement to Analysis Situs
• The current book provides a skillful translation of his [Poincaré's] breakthrough work in algebraic topology. . . . John Stillwell has done a marvelous job with his translations and editing. . . . Poincaré's prose flows smoothly - he was a pretty good writer, after all - and it is a delight to read. . . . I found this a charming contrast to the impersonality of many modern texts.

Bill Satzer, MAA Reviews
• The English translation of Poincaré's celebrated work Analysis situs, together with the series of "Compliments” he added between 1895 and 1904, makes available a remarkable resource to the non-francophone community. Darboux wrote of Poincaré that "when he drafted a memoir, he drafted it in one go, limiting himself to some crossings out, without coming back to what he had written”. Stillwell's translation admits us to this pouring forth of Poincaré's ideas, and to their consequences as played out in the supplements. Not only do we get a glimpse of Poincaré at work, but these papers contain the beginnings of the modern notions used in topology today and the connections they make with the ideas of the nineteenth century.

Analysis situs and its supplements have earned their place as the source of many rich ideas that developed into the field of algebraic topology. At the end of the introduction to Analysis situs Poincaré writes, "I do not think then that I have engaged in useless work in writing the present memoir”. The reader more than a century later will find that he or she will not engage in useless work in reading Poincaré's papers. We have Stillwell to thank for making such work easier with his translation.

John McCleary, Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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