Publication:
A note on fundamental groups of symplectic torus complements in 4-manifolds

dc.contributor.coauthorPark, B. Doug
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorEtgü, Tolga
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T23:44:17Z
dc.date.issued2008
dc.description.abstractPreviously, we constructed an infinite family of knotted symplectic tori representing a fixed homology class in the symplectic four-manifold E(n) K, which is obtained by Fintushel-Stern knot surgery using a nontrivial fibered knot K in S-3, and distinguished the (smooth) isotopy classes of these tori by indirectly computing the Seiberg-Witten invariants of their complements. In this note, we compute the fundamental groups of the complements of these knotted tori and show that for each nontrivial fibered knot K these groups constitute an infinite collection of nonisomorphic groups. We also review some other constructions of symplectic tori in 4-manifolds and show that the fundamental groups of the complements do not distinguish homologous tori in those cases.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue9
dc.description.openaccessNO
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipGEBIP
dc.description.sponsorshipTurkish Academy of Sciences
dc.description.sponsorshipCAREER
dc.description.sponsorshipScientific and Technological Research Council of Turkey
dc.description.sponsorshipCFI
dc.description.sponsorshipNSERC
dc.description.sponsorshipOIT We would like to thank Hans U. Boden, Steven Boyer, Olivier Collin, Andrew Nicas and Stefano Vidussi for their indispensable help in writing the proofs of Lemmas 3.5 and 3.6. Most of this work was completed while the first author was a postdoctoral fellow at McMaster University. The figures were produced by the second author using Adobe (R) Illustrator (R) Version 10. The first author was partially supported by a GEBIP grant of the Turkish Academy of Sciences and a CAREER grant of the Scientific and Technological Research Council of Turkey. The second author was partially supported by CFI, NSERC and OIT grants.
dc.description.volume17
dc.identifier.doi10.1142/S0218216508006567
dc.identifier.eissn1793-6527
dc.identifier.issn0218-2165
dc.identifier.scopus2-s2.0-58149481351
dc.identifier.urihttps://doi.org/10.1142/S0218216508006567
dc.identifier.urihttps://hdl.handle.net/20.500.14288/13639
dc.identifier.wos259544100003
dc.keywords4-manifold
dc.keywordsSymplectic
dc.keywordsIsotopy
dc.keywordsLink surgery
dc.keywordsFiber sum
dc.keywordsFundamental group rational elliptic-surfaces
dc.keywords3-manifolds
dc.keywordsHomology
dc.keywordsSurgery
dc.language.isoeng
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relation.ispartofJournal of Knot Theory and Its Ramifications
dc.subjectMathematics
dc.titleA note on fundamental groups of symplectic torus complements in 4-manifolds
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorEtgü, Tolga
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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