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Smooth surfaces with
non-simply-connected complements
Hee Jung Kim and Daniel Ruberman |
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Algebraic & Geometric Topology 8 (2008) 2263–2287
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Abstract |
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We consider two constructions of surfaces in simply-connected –manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author [Geom. Topol. 10 (2006) 27–56]. We also construct, for any group satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group . In each case, we produce infinitely many smoothly inequivalent surfaces that are equivalent up to smooth –cobordism and hence are topologically equivalent for good groups. |
Keywords
knot, embedded surface, twist-spin, symplectic
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Mathematical Subject Classification 2000
Primary: 57R57
Secondary: 57N13
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References |
Publication
Received: 19 May 2008
Revised: 8 November 2008
Accepted: 29 September 2008
Published: 20 December 2008
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Authors |
| Hee Jung Kim | |
| Louisiana State University Department of Mathematics 396 Lockett Hall Baton Rouge, Louisiana 70803 USA |
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| http://www.math.lsu.edu/~heekim/ | |
| Daniel Ruberman | |
| Brandeis University Department of Mathematics MS 050 Waltham, MA 02454 USA |
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| http://people.brandeis.edu/~ruberman/ | |
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