Knotted surfaces in 4-manifolds
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Thomas E. Mark
Abstract.
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 g 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.
© 2013 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Low-dimensional non-abelian Leibniz cohomology
- Twisted torsion invariants and link concordance
- Groups with faithful irreducible projective unitary representations
- Universality of the Selberg zeta-function for the modular group
- An innocent theorem of Banaschewski, applied to an unsuspecting theorem of De Marco, and the aftermath thereof
- Knotted surfaces in 4-manifolds
- Knot surgery and Scharlemann manifolds
- On the Sato–Tate conjecture on average for some families of elliptic curves
Articles in the same Issue
- Masthead
- Low-dimensional non-abelian Leibniz cohomology
- Twisted torsion invariants and link concordance
- Groups with faithful irreducible projective unitary representations
- Universality of the Selberg zeta-function for the modular group
- An innocent theorem of Banaschewski, applied to an unsuspecting theorem of De Marco, and the aftermath thereof
- Knotted surfaces in 4-manifolds
- Knot surgery and Scharlemann manifolds
- On the Sato–Tate conjecture on average for some families of elliptic curves
