Mathematics > Differential Geometry
[Submitted on 12 Oct 2007 (v1), last revised 6 Nov 2010 (this version, v5)]
Title:Surgery, Yamabe invariant, and Seiberg-Witten theory
View PDFAbstract:By using the gluing formula of the Seiberg-Witten invariant, we compute the Yamabe invariant Y(X) of 4-manifolds X obtained by performing surgeries along points, circles or tori on compact Kaehler surfaces. For instance, if M is a compact Kaehler surface of nonnegative Kodaira dimension, and N is a smooth closed oriented 4-manifold with b_2^+(N)=0 and Y(N)>= 0, then we show that Y(M # N)=Y(M).
Submission history
From: Chanyoung Sung [view email][v1] Fri, 12 Oct 2007 01:28:52 UTC (12 KB)
[v2] Wed, 27 Aug 2008 00:13:46 UTC (15 KB)
[v3] Mon, 29 Sep 2008 01:29:52 UTC (16 KB)
[v4] Wed, 24 Dec 2008 08:56:45 UTC (16 KB)
[v5] Sat, 6 Nov 2010 06:48:48 UTC (16 KB)
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