曲面的二次增强：两个消失结果
Quadratic enhancements of surfaces: two vanishing results
摘要：
本文记录了我们关于低维流形上Pin结构的论文[KT]中莫名其妙地遗漏的两个结果。科比选择不被列为合著者。曲面F上的Pin^-结构导致模2交形式q的二次增强：H_1（F;Z/2 Z）-> Z/4 Z定理1.1说q在与有界3-流形同调的映射的核上为零。Kreck和Puppe（arXiv：0707.1599 [math.AT]）使用了这个方法，他们通过作者发给Kreck的电子邮件来证明。一个更精致和公开的证据似乎是可取的。在[KT]的第6节中，在定向4-流形M^4中与w_2对偶的曲面F上构造了一个Pin^-结构。定理2.1说q在H^1（F;Z/2 Z）中H^1（M^4;Z/2 Z）的像的庞加莱对偶上为零。
英文摘要：
This note records two results which were inexplicably omitted from our paper on Pin structures on low dimensional manifolds, [KT]. Kirby chose not to be listed as a coauthor. A Pin^- structure on a surface F induces a quadratic enhancement of the mod 2 intersection form, q: H_1(F;Z/2Z) -> Z/4Z Theorem 1.1 says that q vanishes on the kernel of the map in homology to a bounding 3-manifold. This is used by Kreck and Puppe (arXiv:0707.1599 [math.AT]) who refer for a proof to an email of the author to Kreck. A more polished and public proof seems desirable. In [KT], section 6, a Pin^- structure is constructed on a surface F dual to w_2 in an oriented 4-manifold M^4. Theorem 2.1 says that q vanishes on the Poincare dual to the image of H^1(M^4;Z/2Z) in H^1(F;Z/2Z).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
