Volume 8, issue 4 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Smooth surfaces with non-simply-connected complements

Hee Jung Kim and Daniel Ruberman

Algebraic & Geometric Topology 8 (2008) 2263–2287
Abstract

We consider two constructions of surfaces in simply-connected 4–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 G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produce infinitely many smoothly inequivalent surfaces that are equivalent up to smooth s–cobordism and hence are topologically equivalent for good groups.

Keywords
knot, embedded surface, twist-spin, symplectic
Mathematical Subject Classification 2000
Primary: 57R57
Secondary: 57N13
References
Publication
Received: 19 May 2008
Revised: 8 November 2008
Accepted: 29 September 2008
Published: 20 December 2008
Authors
Hee Jung Kim
Louisiana State University
Department of Mathematics
396 Lockett Hall
Baton Rouge, Louisiana 70803
USA
http://www.math.lsu.edu/~heekim/
Daniel Ruberman
Brandeis University
Department of Mathematics
MS 050
Waltham, MA 02454
USA
http://people.brandeis.edu/~ruberman/