Homotopy K3 surfaces and mod 2 Seiberg-Witten invariants
Homotopy K3 surfaces and mod 2 Seiberg-Witten invariants
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DOI：
10.4310/mrl.1997.v4.n1.a2
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发表时间：
1997
影响因子：
1
通讯作者：
J. Morgan;Z. Szabó
中科院分区：
文献类型：
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作者：
J. Morgan;Z. Szabó
写这篇论文后，我们了解到，这一结果也知道克朗海默和古田。这个定理与Fintushel和Stern的工作密切相关[FS 1]，[FS 2]。他们证明了任何包含光滑嵌入的SU（2，3，7）的同伦K3曲面都具有模2的非平凡SU（2）唐纳森不变量。注意，定理1.1和民间猜想，（参见。[W])关于唐纳森不变量与Seiberg-Witten不变量之间的关系，将意味着每个同伦K3曲面都有模2的非平凡SU（2）唐纳森不变量.作为定理1.1和Seiberg-Witten基本类[KM]、[MSzT]、[D2]的附加不等式的直接推论，我们得到如下：
After writing this paper we learned that this result was also known to Kronheimer and Furuta. This theorem is closely related to the work of Fintushel and Stern [FS1], [FS2]. They proved that any homotopy K3 surface which contains a smoothly embedded Σ(2, 3, 7) has nontrivial SU(2) Donaldson invariants mod 2. Note that Theorem 1.1 and the folk conjecture, (cf. [W]), on the relation between Donaldson and Seiberg-Witten invariants would imply that every homotopy K3 surface has nontrivial SU(2) Donaldson invariants mod 2. As a straightforward corollary of Theorem 1.1 and the adjunction inequalities for the Seiberg-Witten basic classes [KM], [MSzT], [D2] we get the following: