Table Of Content

C ONTEMPORARY M ATHEMATICS 501 (cid:26)(cid:12)(cid:9)(cid:24)(cid:20)(cid:8)(cid:23)(cid:8)(cid:4)(cid:27)(cid:20)(cid:21)(cid:28)(cid:5)(cid:9)(cid:4)(cid:6)(cid:13)(cid:29)(cid:4) (cid:27)(cid:8)(cid:21)(cid:30)(cid:8)(cid:23)(cid:20)(cid:12)(cid:24)(cid:4)(cid:11)(cid:23)(cid:20)(cid:28)(cid:24)(cid:23)(cid:28)(cid:20)(cid:8)(cid:9) (cid:31)(cid:21)(cid:20) (cid:9)!(cid:21)(cid:5)(cid:4)(cid:21)(cid:13)(cid:4)(cid:26)(cid:12)(cid:9)(cid:24)(cid:20)(cid:8)(cid:23)(cid:8)(cid:4)(cid:27)(cid:20)(cid:21)(cid:28)(cid:5)(cid:9)(cid:4)(cid:6)(cid:13)(cid:29)(cid:4)(cid:27)(cid:8)(cid:21)(cid:30)(cid:8)(cid:23)(cid:20)(cid:12)(cid:24)(cid:4)(cid:11)(cid:23)(cid:20)(cid:28)(cid:24)(cid:23)(cid:28)(cid:20)(cid:8)(cid:9)"(cid:4) #(cid:12)(cid:23)!(cid:4)$(cid:5)(cid:5)(cid:18)(cid:12)(cid:24)(cid:6)(cid:23)(cid:12)(cid:21)(cid:13)(cid:9)(cid:4)%%%(cid:4) &(cid:6)’(cid:4)((cid:2))*(cid:3)"(cid:4)((cid:3)(cid:3)+ ,(cid:21)(cid:20)(cid:23)(cid:20)(cid:12)- "(cid:4).(cid:8)(cid:18)(cid:7)(cid:12)(cid:28)(cid:30) ,(cid:6)(cid:20)(cid:8)(cid:18)(cid:4)(cid:26)(cid:8) (cid:12)(cid:30)(cid:5)(cid:8) /(cid:6)(cid:28)(cid:18)(cid:4)%(cid:7)(cid:21)(cid:29)(cid:23) $(cid:18)(cid:6)(cid:12)(cid:13)(cid:4)0(cid:6)(cid:18)(cid:8)(cid:23)(cid:23)(cid:8) 1(cid:29)(cid:12)(cid:23)(cid:21)(cid:20)(cid:9) American Mathematical Society Discrete Groups and Geometric Structures d 08 n0 a2 ps k, uij or Grort e K ets, re cr su Dict n ru ot op c S hri ksmet r oo We G C ONTEMPORARY M ATHEMATICS 501 Discrete Groups and Geometric Structures Workshop on Discrete Groups and Geometric Structures, with Applications III May 26–30, 2008 Kortrijk, Belgium Karel Dekimpe Paul Igodt Alain Valette Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor George Andrews Abel Klein Martin J. Strauss 2000 Mathematics Subject Classification. Primary 20F67, 20J06, 22E40,30F40, 37E10, 51M10, 53C50, 55R10, 57S25. Library of Congress Cataloging-in-Publication Data InternationalWorkshoponDiscreteGroupsandGeometricStructures,withApplicationsIII(5th: 2008: K.U.LeuvenCampusKortrijk) Discretegroupsandgeometricstructures: 5thInternationalWorkshoponDiscreteGroupsand Geometric Structures, with Applications III, May 2008, K.U. Leuven Campus Kortrijk / Karel Dekimpe,PaulIgodt,AlainValette,editors. p.cm. —(Contemporarymathematics;v.501) Includesbibliographicalreferences. ISBN978-0-8218-4647-6(alk.paper) 1. Discrete groups—Congresses. 2. Geometrical constructions—Congresses. I. Dekimpe, Karel,1967– II.Igodt,Paul,1956– III.Valette,Alain. IV.Title. QA178.I582008 512(cid:1).2—dc22 2009026844 Copying and reprinting. Materialinthisbookmaybereproducedbyanymeansfor edu- cationaland scientific purposes without fee or permissionwith the exception ofreproduction by servicesthatcollectfeesfordeliveryofdocumentsandprovidedthatthecustomaryacknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercialuseofmaterialshouldbeaddressedtotheAcquisitionsDepartment,AmericanMath- ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can [email protected]. Excludedfromtheseprovisionsismaterialinarticlesforwhichtheauthorholdscopyright. In suchcases,requestsforpermissiontouseorreprintshouldbeaddresseddirectlytotheauthor(s). (Copyrightownershipisindicatedinthenoticeinthelowerright-handcornerofthefirstpageof eacharticle.) (cid:1)c 2009bytheAmericanMathematicalSociety. Allrightsreserved. TheAmericanMathematicalSocietyretainsallrights exceptthosegrantedtotheUnitedStatesGovernment. Copyrightofindividualarticlesmayreverttothepublicdomain28years afterpublication. ContacttheAMSforcopyrightstatusofindividualarticles. PrintedintheUnitedStatesofAmerica. (cid:1)∞ Thepaperusedinthisbookisacid-freeandfallswithintheguidelines establishedtoensurepermanenceanddurability. VisittheAMShomepageathttp://www.ams.org/ 10987654321 141312111009 Contents Preface vii List of Participants ix Complex hyperbolic lattices John R. Parker 1 Rank-one isometries of proper CAT(0)-spaces Ursula Hamensta¨dt 43 Trace polynomial for simple loops on the twice punctured torus Raquel A´gueda 61 Simplicial volume of products and fiber bundles Michelle Bucher 79 Homology of Hantzsche-Wendt groups Karel Dekimpe and Nansen Petrosyan 87 Seifert fibred structure and rigidity on real Bott towers Yoshinobu Kamishima and Admi Nazra 103 Exotic circles in groups of piecewise smooth circle homeomorphisms Abdelhamid Adouani and Habib Marzougui 123 Groups generated by spine reflections admitting crooked fundamental domains Virginie Charette 133 v This page intentionally left blank Preface The 2008 editionof “DiscreteGroups andGeometric Structures”, heldat Kor- trijk from May 26 to May 30, was the fifth in a series which started in 1996, and takesplaceevery3years. Eightinvitedone-hourtalks,6extraplenarytalksand30 talks in parallel sessions have allowed the more than seventy participants to learn about the present state-of-the-art in research linking group theory, geometry and topology. Not more than a remarkable coincidence was the fact that the workshop took placeveryshortlyaftertheAbelPrizewasawardedtoJohnThompsonandJacques Tits who, by their truly outstanding work for decades, have shown the power, beautyandintimaterelationshipbetweendiscretegroupsandgeometricstructures. Themathematicaloutlineoftheconference,shapedbythemaininvitedspeak- erswiththeirinspiringtalks,examplesand(open)problems, presentsaveryactive domain of on-going interdisciplinary research. The organisers, hence, have a feeling that the conference succesfully met the aims they had in mind: presenting high-level state-of-the-art research mathemat- ics in a stimulating atmosphere of dialogue and collaboration, and with special attention toward young researchers. Research in discrete groups and geometric structures is clearly alive and kicking! Let us say thank you, to all speakers and participants. And, for sure, thank you also to all participants who contributed to this volume with their research work and results. Onbehalfoftheorganisingcommitteeswewanttoexpressourgratitudealsoto thesupportingorganisationsforthismeeting,i.e. theFundforScientificResearch– Flanders, the Fonds National de la Recherche Scientifique, the F.W.O. Research Network “Fundamental methods and techniques in Mathematics”, the Katholieke UniversiteitLeuven(CampusKortrijk),theUniversit´eCatholiquedeLouvain, and finally the American Mathematical Society Contemporary Mathematics Editorial Board. It is with gratitude and recognition to all participants, speakers, authors and refereesthatwepresentthisvolumeandinvitereaderstoconsider DiscreteGroups and Geometric Structures as an inspiring topic. Paul Igodt On behalf of the organising committees and the editors K.U. Leuven Campus Kortrijk June 2009 vii This page intentionally left blank List of Participants Raquel A´gueda Mate, Universidad de Mathieu Carette Castilla - La Mancha, Spain Universit´e Libre de Bruxelles, Belgium Jørgen Andersen, Aarhus Universitet, Virginie Charette Denmark Universit´e de Sherbrooke, Canada Daniel Appel Frank De Clerck H.Heine-Universita¨t, Du¨sseldorf, Ghent University, Belgium Germany Karel Dekimpe Thierry Barbot K.U. Leuven, Belgium ENS, Lyon, France Pierre de la Harpe Udo Baumgartner Universit´e de Gen`eve, Switzerland University of Newcastle, Australia Tom De Medts Rolf Bienert Ghent University, Belgium H.Heine-Universita¨t, Du¨sseldorf, Steven Deprez Germany K.U. Leuven, Belgium Adara-Monica Blaga Sandra Deschamps Universitatea de Vest Timi¸sora, K.U. Leuven, Belgium Romania Dennis Dreesen Marc Bourdon K.U. Leuven, Belgium Universit´e de Lille, France Bruno Duchesne Martin Bridson Universit´e de Gen`eve, Switzerland University of Oxford, United Kingdom Christopher Dwyer Michelle Bucher-Karlsson SUNY at Binghamton, USA Kungliga Tekniska h¨ogskolan Stockholm, Sweden Aziz El Kacimi Universit´e de Valenciennes, France Dietrich Burde Universita¨t Wien, Austria S´ebastien Falgui`eres K.U. Leuven, Belgium Leandro Cagliero Universidad Nacional de Co´rdoba, Benson Farb Argentina University of Chicago, USA Pierre-Emmanuel Caprace Yves F´elix IHES, Paris, France UC Louvain, Belgium ix

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