Discrete Groups and Geometric Structures: Workshop on Discrete Groups and Geometric Structures, With Applications Iii: May 26-30, 2008: Kortrijk, Belgium

162 Pages·2009·1.58 MB·English

by  Karel Dekimpe, Paul Igodt, Alain Valette (ed.)

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