Higher Type Adjunction Inequalities in Seiberg-Witten Theory

By Peter S. Ozsv'ath, Zolt'an Szab'o. 2000

55 citations recorded by the source corpus.

In this paper, we derive new adjunction inequalities for embedded surfaces with non-negative self-intersection number in four-manifolds. These formulas are proved by using relations between Seiberg-Witten invariants which are induced from embedded surfaces. To prove these relations, we develop the relevant parts of a Floer theory for four-manifolds which bound circle-bundles over Riemann surfaces.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/153793432c17adcee4edcc12e29971e47acac731

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Link cobordisms and absolute gradings in link Floer homology (2017, methodology): “ generally, one could put more exotic sets of divides on and consider the U= 1 and V = 1 reductions of the associated link cobordism maps, and try to recover the higher type adjunction relations from [OS00a], which Ozsvath and Szabo proved for the Seiberg{Witten invariant. We note that applying Theo”
Holomorphic disks and three-manifold invariants: Properties and applications (2001, background): “It is easy to see from [25], see also [26], that the irreducible solutions and θ are all transversally cut out by the equations.”
Ricci curvature, minimal volumes, and Seiberg-Witten theory (2000, methodology): “The proof is a direct extension of the computations in [30], although for ` > 0 we now use the holonomy-constrained Seiberg-Witten invariant of [32]; cf.”
Holomorphic disks and topological invariants for closed three-manifolds (2001, methodology): “e Spin C structures determined by the line-bundles E, K⊗ E−1 respectively. In order to simplify the computation we will use a certain perturbation of the SeibergWitten equation. Using the notation of [33] this perturbation depends on a real parameter u, and corresponds to adding a two-form iu(∗dη) t”
Constructing infinitely many smooth structures on small 4‐manifolds (2007, background): “[19]) to all these surfaces, we conclude the following:”