关于2-配合物的普遍配对

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-06-26 DOI:10.1112/blms.70130

Mikhail Khovanov, Vyacheslav Krushkal, John Nicholson

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引用次数: 0

摘要

在Freedman， Kitaev, Nayak, Slingerland， Walker和Wang， J. Geom中定义了流形的普遍配对，并证明了它在4维上缺乏正性。[j].植物学报，2005,23(3):393 - 397。我们证明了2-配合物的类似结果，并证明了普适配对不能检测到简单同伦等价与3-变形的区别。对于2-配合物，这两种等价关系是否不同的问题是Andrews-Curtis猜想的主题。我们还讨论了高维配合物的普遍配对，并证明了它是不正的。

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On the universal pairing for 2-complexes

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On the universal pairing for 2-complexes

The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 in [Freedman, Kitaev, Nayak, Slingerland, Walker, and Wang, J. Geom. Topol. 9 (2005), 2303–2317]. We prove an analogous result for 2-complexes, and show that the universal pairing does not detect the difference between simple homotopy equivalence and 3-deformations. The question of whether these two equivalence relations are different for 2-complexes is the subject of the Andrews–Curtis conjecture. We also discuss the universal pairing for higher dimensional complexes and show that it is not positive.

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