Perspectives in Analysis, Geometry, and Topology: On the Occasion of the 60th Birthday of Oleg Viro

486 Pages·2012·7.442 MB·English

by  Selman Akbulut (auth.), Ilia Itenberg, Burglind Jöricke, Mikael Passare (eds.)

Progress in Mathematics
Volume296
SeriesEditors
HymanBass
JosephOesterle´
YuriTschinkel
AlanWeinstein
Forfurthervolumes:
http://www.springer.com/series/4848
Ilia Itenberg • Burglind Jo¨ricke • Mikael Passare
Editors
Perspectives in Analysis,
Geometry, and Topology
On the Occasion of the 60th Birthday
of Oleg Viro
Editors
IliaItenberg BurglindJo¨ricke
Universite´PierreetMarieCurie InstitutdesHautesE´tudesScientifiques
andInstitutUniversitairedeFrance LeBois-Marie
InstitutdeMathe´matiquesdeJussieu 35,routedeChartres
4placeJussieu Bures-sur-Yvette91440
75005Paris France
France [email protected]
[email protected]
MikaelPassare
DepartmentofMathematics
StockholmUniversity
StockholmSE-10691
Sweden
[email protected]
ISBN978-0-8176-8276-7 e-ISBN978-0-8176-8277-4
DOI10.1007/978-0-8176-8277-4
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011939742
Mathematics Subject Classification (2010): 11H06, 14P25, 14T05, 14H99, 20F36, 31A25, 32U05,
53D05,53D10,53D40,53D42,57Mxx,57M25,57M27
(cid:2)c SpringerScience+BusinessMedia,LLC2012
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permission ofthe publisher (Springer Science+Business Media, LLC,233Spring Street, New York,
NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein
connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,
orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.birkhauser-science.com)
ThisvolumeisdedicatedtoOlegViroontheoccasionofhis60thbirthday.

Contents
Preface............................................................................ ix
AGlimpseintoViro’sWork ................................................... xi
OntheContentofThisVolume................................................ xv
ProgramoftheSymposium.................................................... xxv
OntheUnityofMathematics.................................................. xxix
ExoticStructuresonSmoothFour-Manifolds ............................... 1
SelmanAkbulut
RationalLinkingandContactGeometry .................................... 19
KennethBakerandJohnEtnyre
Regularityof Plurisubharmonic Upper Envelopes in Big
CohomologyClasses ............................................................ 39
RobertBermanandJean-PierreDemailly
TowardaGeneralizedShapiroandShapiroConjecture................... 67
AlexDegtyarev
OntheNumberofComponentsofaCompleteIntersection
ofRealQuadrics................................................................. 81
AlexDegtyarev,IliaItenberg,andViatcheslavKharlamov
RationalSFT, LinearizedLegendrianContactHomology,
andLagrangianFloerCohomology........................................... 109
TobiasEkholm
TopologyofSpacesofS-Immersions.......................................... 147
YakovEliashbergandNikolaiMishachev
vii
viii Contents
OnContinuityofQuasimorphismsforSymplecticMaps .................. 169
MichaelEntov,LeonidPolterovich,PierrePy,
withanAppendixbyMichaelKhanevsky
OnSymplecticCaps ............................................................ 199
DavidT.GayandAndra´sI.Stipsicz
Cauchy–Pompeiu-TypeFormulasfor∂¯ onAffineAlgebraic
RiemannSurfacesandSomeApplications................................... 213
GennadiM.Henkin
RemarksonKhovanovHomologyandthePottsModel.................... 237
LouisH.Kauffman
AlgebraicEquationsandConvexBodies..................................... 263
KiumarsKavehandAskoldKhovanskii
FloerHomologyontheExtendedModuliSpace ............................ 283
CiprianManolescuandChristopherWoodward
Projective Algebraicity of Minimal Compactifications
ofComplex-HyperbolicSpaceFormsofFiniteVolume..................... 331
NgaimingMok
Some Examples of Real Algebraic and Real
PseudoholomorphicCurves.................................................... 355
StepanYu.Orevkov
Schur–Weyl-TypeDualityforQuantizedgl(1|1),theBurau
RepresentationofBraidGroups,andInvariantsofTangledGraphs..... 389
NicolaiReshetikhin,CatharinaStroppel,andBenWebster
KhovanovHomologyTheoriesandTheirApplications..................... 403
AlexanderShumakovitch
TropicalandAlgebraicCurveswithMultiplePoints ....................... 431
EugeniiShustin
Preface
Encountersbetweenthe fieldsofanalysis, geometry,andtopologyare widespread
and often provide major impetus for breakthroughsin these domains. Recent de-
velopmentsinlow-dimensionaltopology,algebraicgeometry,symplecticgeometry,
complexanalysis,andtropicalgeometryaresorichwithimpressiveexamplesthat
any attempt to reflect a major portion of them in a single volume would be too
ambitious.
Forexample,recentexcitingprogressinlow-dimensionaltopologyandgeometry
would have been unthinkable without powerful techniques from analysis; new
achievementsintopologyandsymplecticgeometryhavebeeninfluencingcomplex
analysis; methodsof tropical geometryare being used in algebraic geometry,sta-
tisticalphysics,andcomplexanalysis;differentialequationscomingfromcomplex
analysishaveapplicationsinalgebraicgeometry.
The variety of topics presented by leading experts in this volume should
nonetheless give some sense of recent developments in these fields and their
interactionswithoneanother.
A Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry,and
TopologywasheldatStockholmUniversityinMay2008.Thechoiceofsubjectsfor
thissymposiumandthisvolumewasmotivatedbytheworkandthemathematical
interests of Oleg Viro, to whom the symposium and this collection are dedicated.
As a mathematician with broad education and interests, Viro has a deep feeling
for the unity of mathematics. Viro is famous for fundamental results in several
areas of geometry and topology. As a professor at Uppsala University, Viro has
madeinvaluablecontributionstoSwedishresearchbycomplementingthecountry’s
longstandingtraditioninanalysiswithhisownrenownedexpertiseingeometryand
topology.
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