Details

Autor(en) / Beteiligte

• Mark, Thomas E.

Titel

Knotted surfaces in 4-manifolds

Ist Teil von

• Forum mathematicum, 2013-05, Vol.25 (3), p.597-637

Ort / Verlag

Berlin: Walter de Gruyter GmbH

Erscheinungsjahr

2013

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Fintushel and Stern have proved that if is a symplectic surface in a symplectic 4-manifold such that has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent but smoothly distinct embedded surfaces homologous to . Here we extend this result to include symplectic surfaces whose self-intersection is bounded below by , where is the genus of . We make use of tools from Heegaard Floer theory, and include several results that may be of independent interest. Specifically we give an analogue for Ozsváth–Szabó invariants of the Fintushel–Stern knot surgery formula for Seiberg–Witten invariants, both for closed 4-manifolds and manifolds with boundary. This is based on a formula for the Ozsváth–Szabó invariants of the result of a logarithmic transformation, analogous to one obtained by Morgan–Mrowka–Szabó for Seiberg–Witten invariants, and the results on Ozsváth–Szabó invariants of fiber sums due to the author and Jabuka. In addition, we give a calculation of the twisted Heegaard Floer homology of circle bundles of “large” degree over Riemann surfaces.