Curvature, Connected Sums, and Seiberg-Witten Theory

2001/11/20 by Masashi Ishida, Claude LeBrun, Ishida, Masashi +1
Mathematics · #53C23 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:53C23 #msc:57R57

paper · pdf · doi:10.48550/arxiv.math/0111228

29 pages, LaTeX2e. Final version, to appear in Communications in Analysis and Geometry. Additions include expanded discussion of foundational material concerning the Bauer-Furuta invariant and monopole classes

arxiv created 2003/06/04 · arxiv updated 2009/11/30

Abstract

We consider several differential-topological invariants of compact 4-manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta, we compute these invariants in many cases that were previously intractable. In particular, we are now able to calculate the Yamabe invariant for certain connected sums of complex surfaces.

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