Quadratic enhancements of surfaces: two vanishing results - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: This note records two results which were inexplicably omitted from our paperon Pin structures on low dimensional manifolds, KT. Kirby chose not to belisted as a coauthor.A Pin^- structure on a surface F induces a quadratic enhancement of the mod 2intersection form, q: H 1F;Z-2Z -> Z-4ZTheorem 1.1 says that q vanishes on the kernel of the map in homology to abounding 3-manifold. This is used by Kreck and Puppe arXiv:0707.1599math.AT who refer for a proof to an email of the author to Kreck. A morepolished and public proof seems desirable.In KT, section 6, a Pin^- structure is constructed on a surface F dual tow 2 in an oriented 4-manifold M^4. Theorem 2.1 says that q vanishes on thePoincare dual to the image of H^1M^4;Z-2Z in H^1F;Z-2Z.



Author: Laurence R. Taylor

Source: https://arxiv.org/







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