Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfaces

Details Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfaces Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfaces

2004-01-26

arxiv.org/abs/math/0401345v2

Mathematics

Geometric Topology

18 pages, 1 figure, editing: a few improvements, more detailed proofs in section 3

Scientific paper

We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinements of the usual Seiberg-Witten and Ozsvath-Szabo invariants. We prove for instance the adjunction inequality for membranes, which estimates their genus.

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