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

Finashin S.

arXiv, no.No, pp.1-18, 2004 (Non Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2004
  • Journal Name: arXiv
  • Page Numbers: pp.1-18
  • Middle East Technical University Affiliated: Yes

Abstract

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.