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Philip Hackney Marcy Robertson Donald Yau

Infinity Properads and Infinity Wheeled Properads

Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and NY Catharina Stroppel, Bonn Anna Wienhard, Heidelberg

2147

More information about this series at http://www.springer.com/series/304

Philip Hackney • Marcy Robertson • Donald Yau

Infinity Properads and Infinity Wheeled Properads

123

Marcy Robertson University of California Los Angeles, CA USA

Philip Hackney Stockholm University Stockholm, Sweden

Donald Yau Ohio State University, Newark Campus Newark, OH USA

ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-20546-5 DOI 10.1007/978-3-319-20547-2

ISSN 1617-9692

(electronic)

ISBN 978-3-319-20547-2

(eBook)

Library of Congress Control Number: 2015948871 Mathematics Subject Classification (2010): 18D15, 18D50, 55P48, 55U10 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)

To Chloë and Elly To Rosa To Eun Soo and Jacqueline

Preface

This monograph fits in the intersection of two long and intertwined stories. The first part of our story starts in the mid-twentieth century, when it became clear that a new conceptual framework was necessary for the study of higher homotopical structures arising in algebraic topology. Some better known examples of these higher homotopical structures appear in work of J.F. Adams and S. Mac Lane [Mac65] on the coproduct in the bar construction and work of J. Stasheff [Sta63], J.M. Boardman and R.M. Vogt [BV68, BV73], and J.P. May [May72] on