Algebraic Topology of Finite Topological Spaces and Applications
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful to
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2032
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Jonathan A. Barmak
Algebraic Topology of Finite Topological Spaces and Applications
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Jonathan A. Barmak Departamento de Matem´atica Fac. Cs. Exactas y Naturales Universidad de Buenos Aires Ciudad Universitaria Pabell´on I (1428) Ciudad de Buenos Aires Argentina
ISBN 978-3-642-22002-9 e-ISBN 978-3-642-22003-6 DOI 10.1007/978-3-642-22003-6 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2011934806 Mathematics Subject Classification (2010): 55-XX; 05-XX; 52-XX; 06-XX; 57-XX c Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
A las dos bobes
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Preface There should be more math. This could be mathier. B.A. Summers
This book is a revised version of my PhD Thesis [5], supervised by Gabriel Minian and defended in March 2009 at the Mathematics Department of the Facultad de Ciencias Exactas y Naturales of the Universidad de Buenos Aires. Some small changes can be found here, following the suggestions of the referees and the editors of the LNM. Gabriel proposed that we work together in the homotopy theory of finite spaces at the beginning of 2005, claiming that the topic had great potential and could be rich in applications. Very soon I became convinced of this as well. A series of notes by Peter May [51–53] and McCord and Stong’s foundational papers [55, 76] were the starting point of our research. May’s notes contain very interesting questions and open problems, which motivated the first part of our work. This presentation of the theory of finite topological spaces includes the most fundamental ideas and results previous to our work and, mainly, our contributions over the last years. It is intended for topologists and combinatorialists, but since it is a self-contained exposition, it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology. The revisions of this book were made during a postdoc at Kungli
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