Simplicial Structures in Topology
Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is dev
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Davide L. Ferrario
•
Renzo A. Piccinini
Simplicial Structures in Topology
ABC
Dr. Davide L. Ferrario Universit`a di Milano-Bicocca Dipartimento di Matematica e Applicazioni Via R. Cozzi 53 20125 Milano Italy [email protected]
Dr. Renzo A. Piccinini Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, B3H 3J5 Canada [email protected]
Editors-in-Chief R´edacteurs-en-chef K. Dilcher K. Taylor Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, B3H 3J5 Canada [email protected]
ISSN 1613-5237 ISBN 978-1-4419-7235-4 e-ISBN 978-1-4419-7236-1 DOI 10.1007/978-1-4419-7236-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010936303 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Albrecht Dold, friend and mentor.
Foreword to the English Edition
Except for a few added comments, this is a faithful translation of the book Strutture simpliciali in topologia, published by Pitagora Editrice, Bologna 2009, as part of the collection Quaderni of the Italian Mathematical Union. It should be noted that this book is neither a comprehensive text in algebraic topology nor is it a monograph on simplicial objects in the modern sense. Its focus is instead on the role of finite simplicial structures, and the algebraic topology deriving from them. We wish to thank Maria Nair Piccinini, who carefully and expertly translated the Italian monograph. We should also thank Karl Dilcher for suggesting and working toward its inclusion in the monograph series of the Canadian Mathematical Society. Finally, we thank Marcia Bunda, Assitant Editor, and Vaishali Damle, Senior Editor of Springer for managing all the technical and bureaucratic aspects of the publication.
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Preface
On a dit, e´ crivais je (ou a` peu pr`es) dans une pr´eface, que la g´eometrie est l’art de bien raisonner sur des figures mal faites. H ENRI P OINCAR E´ [28]
In 1954, One hundred years after Henri Poincar´e’s birth, there was a special session during the International Congress of Mathematics, in the Netherlands, in honor of this great mathematician. The Russia
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