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