论文标题
软木塞的新好奇心
New curiosities in the menagerie of corks
论文作者
论文摘要
软木是一种平滑，可签名，定向，紧凑的4-manifold $ w $，以及边界3个manifold的自diffeomormormormormormormormist $ f $，无法扩展到$ w $的自diffeomormorphism；据说，如果$ f $无法扩展到以$ \ partial w $界定的任何光滑整数同源球的自变态型，则软木塞是强的。令人惊讶的是Dai，Hedden和Mallick的作品表明，文献中大多数著名的软木塞都很强大。我们构建了第一个非挥舞的软木塞，这也引起了绝对异国情调的Mazur歧管的新例子。此外，我们给出了第一个软木塞的例子，其中$ \ a部分w $的差异性可以作为定向反向。
A cork is a smooth, contractible, oriented, compact 4-manifold $W$ together with a self-diffeomorphism $f$ of the boundary 3-manifold that cannot extend to a self-diffeomorphism of $W$; the cork is said to be strong if $f$ cannot extend to a self-diffeomorphism of any smooth integer homology ball bounded by $\partial W$. Surprising recent work of Dai, Hedden, and Mallick showed that most of the well-known corks in the literature are strong. We construct the first non-strong corks, which also give rise to new examples of absolutely exotic Mazur manifolds. Additionally we give the first examples of corks where the diffeomorphism of $\partial W$ can be taken to be orientation-reversing.
