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1 FOLIATIONS 2012

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3 FOLIATIONS 2012 Proceedings of the International Conference Łódź, Poland June 2012 editors Paweł Walczak Uniwersytet Łódzki, Poland Jesús Álvarez López Universidade de Santiago de Compostela, Spain Steven Hurder University of Illinois at Chicago, USA Rémi Langevin Université de Bourgogne, France Takashi Tsuboi University of Tokyo, Japan World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI

4 Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore USA office: 27 Warren Street, Suite , Hackensack, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. FOLIATIONS 2012 Proceedings of the International Conference Copyright 2013 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN Printed in Singapore

5 v Preface This volume contains a set of papers written by the participants (and their colleagues who wished but could not participate) of the international conference Foliations 2012, a satellite event of the 6th European Congress of Mathematics (Kraków, Poland, July 2 7, 2012) held at the Faculty of Mathematics and Computer Science of the University of Lódź (Poland) between June 25 and June 30, The conference was sponsored by the Faculty of Mathematics and Computer Science of the University of Lódź, the Japan Society for Promotion of Science, the National Science Center of Poland, Polish Academy of Sciences, the Stefan Banach International Mathematical Center in Warsaw and the City of Lódź. Participants numbered in approximately 60, about 40 of them from abroad (Brazil, Czech Republic, France, Germany, Israel, Japan, Romania, Russia, Spain and USA). The organizing committee consisted of five people who became editors of this volume and Robert Wolak, a member of the Executive Organizing Committee of the 6ECM. They were supported by the staff of the Faculty of Mathematics and Computer Science and a group of young mathematicians and students from the University of Lódź. The volume is organized similarly to that of Foliations 2005 published by World Scientific Publ. Co. Pte. Ltd. in 2006 (ISBN ). As therein, the papers contained in this volume are closely related to the lectures given at the conference, which was designed to cover various aspects of the theory of foliations, focusing on topology, geometry and dynamics of such objects. All the papers contained in this volume were refereed by experts. Most of them are research papers containing original results, some contain surveys which bring light to the current state of some aspects of the foliation theory, some are of mixed-type (surveys with a bit of new results). The volume contains also a list of open problems presented during the conference at the problem session, then collected and prepared for publication by one of the editors of the volume. We hope that both, the conference itself and this volume of proceedings, should make a significant contribu-

6 vi Preface tion to the progress of our field of science. We express our gratitude to the participants, the contributors of this volume, the sponsors and all the colleagues and students who helped us while organizing the conference and preparing the volume for publication. In particular, we would like to mention Marek Badura (who organized the www-page of the conference as well as the participants data base), Maciej Czarnecki and Szymon Walczak (the secretaries of the organizing committee), and Zofia Walczak (who produced the final TeX-file of the volume). The Editors

7 vii Foliations 2012 Lódź, June 25 30, 2012, Poland 6th European Congress of Mathematics satellite conference Organizing Committees Scientific committee Jesús A. Álvarez López Universidade de Santiago de Compostela, Spain Steven Hurder University of Illinois at Chicago, United States Rémi Langevin Université de Bourgogne, France Takashi Tsuboi University of Tokyo, Japan Pawe l Walczak Uniwersytet Lódzki, Poland Robert Wolak Uniwersytet Jagielloński Local organizers Marek Badura Uniwersytet Lódzki, Poland Maciej Czarnecki Uniwersytet Lódzki, Poland Pawe l G. Walczak Uniwersytet Lódzki, Poland Szymon M. Walczak Uniwersytet Lódzki, Poland Zofia Walczak Uniwersytet Lódzki, Poland

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9 ix Contents Preface Organizing Committees v vii Characterization of the uniform perfectness of diffeomorphism groups preserving a submanifold 1 Kōjun Abe & Kazuhiko Fukui Recent progress in geometric foliation theory 9 Marek Badura & Maciej Czarnecki A class of dimensional type estimations of topological entropy of groups and pseudogroups 23 Andrzej Biś The sutured Thurston norm 41 John Cantwell & Lawrence Conlon Foliations of S 3 by Dupin cyclides 67 Rémi Langevin & Jean-Claude Sifre Transverse invariant measures extend to the ambient space 103 Carlos Meniño Cotón On a Poincaré lemma for foliations 115 Eva Miranda & Romero Solha Compact generation for topological groupoids 139 Nicolas Raimbaud

10 x Contents Prescribing the positive mixed scalar curvature of totally geodesic foliations 163 Vladimir Rovenski & Leonid Zelenko Tautness and the Godbillon-Vey class of foliations 205 Pawe l G. Walczak Local and global stability of leaves of conformal foliations 215 Nina I. Zhukova Problem set 235 Steven Hurder List of Participants 257 Program 261 Author Index 265