论文标题
三角类别中的渐近转移数字
Asymptotic shifting numbers in triangulated categories
论文作者
论文摘要
我们介绍了不变的数字，这些数字衡量了三角类别的自动等效性在类别内转化的渐近量。不变性类似于在动态系统中广泛使用的繁殖性翻译数字。我们还确定，在某些示例中，转移数字对自动等量组的拟态性提供了绝对形态。此外，我们将转移数字与Dimitrov，Haiden，Katzarkov和Kontsevich引入的熵函数联系起来。
We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that are widely used in dynamical systems. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Additionally, we relate our shifting numbers to the entropy function introduced by Dimitrov, Haiden, Katzarkov, and Kontsevich.
