Smooth surfaces with non-simply-connected complements

Kim, Hee Jung¹ ; Ruberman, Daniel²

¹Louisiana State University, Department of Mathematics, 396 Lockett Hall, Baton Rouge, Louisiana 70803, USA
²Brandeis University, Department of Mathematics, MS 050, Waltham, MA 02454, USA

Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2263-2287

Résumé

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.

Détail

DOI : 10.2140/agt.2008.8.2263

Keywords: knot, embedded surface, twist-spin, symplectic

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