Simplicial Complexes of Graphs
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set,
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Jakob Jonsson
Simplicial Complexes of Graphs
1928
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1928
Jakob Jonsson
Simplicial Complexes of Graphs
ABC
Jakob Jonsson Department of Mathematics KTH Lindstedtsvägen 25 10044 Stockholm Sweden [email protected]
ISBN 978-3-540-75858-7
e-ISBN 978-3-540-75859-4
DOI 10.1007/978-3-540-75859-4 Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2007937408 Mathematics Subject Classification (2000): 05E25, 55U10, 06A11 c 2008 Springer-Verlag Berlin Heidelberg 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: design & production GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com
Preface
This book is a revised version of my 2005 thesis [71] for the degree of Doctor of Philosophy at the Royal Institute of Technology (KTH) in Stockholm. The whole idea of writing a monograph about graph complexes is due to Professor Anders Bj¨ orner, my scientific advisor. I am deeply grateful for all his comments, remarks, and suggestions during the writing of the thesis and for his very careful reading of the manuscript. I spent the first years of my academic career at the Department of Mathematics at Stockholm University with Professor Svante Linusson as my advisor. He is the one to get credit for introducing me to the field of graph complexes and also for explaining the fundamentals of discrete Morse theory, the most important tool in this book. Most of the work presented in Chapters 17 and 20 was carried out under the inspiring supervision of Linusson. The opponent (critical examiner) of my thesis defense was Professor John Shareshian; the examination committee consisted of Professor Boris Shapiro, Professor Richard Stanley, and Professor Michelle Wachs. I am grateful for their valuable feedback that was of great help to me when working on this revision. The work of transforming the thesis into a book took place at the Technische Universit¨ at Berlin and the Massachusetts Institute of Technology. I thank Bj¨ orner and Professor G¨ unter Ziegler for encouraging me to submit the manuscript to Springer. Some chapters in this book appear in r
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