Self-Gluing formula of the monopole invariant and its application

2017/09/19 by Gahye Jeong, Jeong, Gahye
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1709.06322

arxiv created 2017/09/19 · arxiv updated 2017/09/20

Abstract

Given a 4-manifold M and two homeomorphic surfaces Σ₁, Σ₂ smoothly embedded in M with genus more than 1, we remove the neighborhoods of the surfaces and obtain a new 4-manifold M from gluing two boundaries S¹ × Σ₁ and S¹ × Σ₁. In this artice, we prove a gluing formula which describes the relation of the Seiberg-Witten invariants of M and M. Moreover, we show the application of the formula on the existence condition of the symplectic structure on a family of 4-manfolds under some conditions.

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