眶褶和奇异光滑R上的Gerbes ^[4]
Gerbes on orbifolds and exotic smooth R^4
摘要：
利用叶理与奇异R^4之间的关系，可以将由盖尔贝变形的轨道折叠$K$理论解释为来自R^4光滑性的变化。我们给出了S^3上积分三阶上同调类的各种解释，并讨论了大奇异R^4和小奇异R^4之间的区别。然后，我们证明了S^3的勒雷轨道的格贝变形的$K$ -理论与某些奇异光滑R^4是一一对应的。等价性可以理解为S^{3}上丛格贝的稳定同构类，其余维1叶理生成Akbulut软木边界的叶理，唯一对应于这些奇异的R^{4}。给定SU（2）通过共轭作用于自身的轨道$SU(2)\times SU(2)\rightrightarrows SU(2)$，等变$K$ -理论在这个轨道上被$H_{SU(2)}^{3}(SU(2),\mathbb{Z})$的元素所变形，对应于R ^[4]上合适的奇异光滑结构的变化。
英文摘要：
By using the relation between foliations and exotic R^4, orbifold $K$-theory deformed by a gerbe can be interpreted as coming from the change in the smoothness of R^4. We give various interpretations of integral 3-rd cohomology classes on S^3 and discuss the difference between large and small exotic R^4. Then we show that $K$-theories deformed by gerbes of the Leray orbifold of S^3 are in one-to-one correspondence with some exotic smooth R^4's. The equivalence can be understood in the sense that stable isomorphisms classes of bundle gerbes on S^{3} whose codimension-1 foliations generates the foliations of the boundary of the Akbulut cork, correspond uniquely to these exotic R^{4}'s. Given the orbifold $SU(2)\times SU(2)\rightrightarrows SU(2)$ where SU(2) acts on itself by conjugation, the deformations of the equivariant $K$-theory on this orbifold by the elements of $H_{SU(2)}^{3}(SU(2),\mathbb{Z})$, correspond to the changes of suitable exotic smooth structures on R^4.
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