论文标题
非零正方形的双重
Duals of non-zero square
论文作者
论文摘要
在简短的说明中，对于每个非零整数n，我们构建了一个4个manifold，其中包含一对平稳的一对球，具有正方形n的常见双重双，但没有自动形态，将一个球带到另一个领域。我们的示例除了表明双重方面的零假设在Gabai's和Schneiderman-teichner在4D灯泡定理中的版本中还具有有趣的特征，它具有Freedman-Quinn和Kervaire-Milnor的一对球体的不变性。由于Akbulut-Matveyev和与著名的Mazur Cork有关的Akbulut-Matveyev和Auckly-Kim-Melvin-Ruberman，证明具有令人惊讶的结果。
In this short note, for each non-zero integer n, we construct a 4-manifold containing a smoothly concordant pair of spheres with a common dual of square n but no automorphism carrying one sphere to the other. Our examples, besides showing that the square zero assumption on the dual is necessary in Gabai's and Schneiderman-Teichner's versions of the 4D Light Bulb Theorem, have the interesting feature that both the Freedman-Quinn and Kervaire-Milnor invariant of the pair of spheres vanishes. The proof gives a surprising application of results due to Akbulut-Matveyev and Auckly-Kim-Melvin-Ruberman pertaining to the well-known Mazur cork.
