论文标题
大小，同源性和惠特尼（Whitney Twist）
Magnitude, homology, and the Whitney twist
论文作者
论文摘要
大小是公制空间和图形的数字不变性，从精确的意义上讲，类似于Euler的特征。幅度同源性是构建用于分类幅度的代数不变式。图形大小的重要特征之一是它相对于称为惠特尼扭曲的操作的行为。我们在惠特尼（Whitney）的曲折下对幅度的不变性进行了同源描述，从而扩展了先前已知的结果，以涵盖大量较宽的粘土。除了提供用于计算大小的新工具外，这是第一个关于使用幅度同源性证明的幅度的新定理。
Magnitude is a numerical invariant of metric spaces and graphs, analogous, in a precise sense, to Euler characteristic. Magnitude homology is an algebraic invariant constructed to categorify magnitude. Among the important features of the magnitude of graphs is its behaviour with respect to an operation known as the Whitney twist. We give a homological account of magnitude's invariance under Whitney twists, extending the previously known result to encompass a substantially wider class of gluings. As well as providing a new tool for the computation of magnitudes, this is the first new theorem about magnitude to be proved using magnitude homology.
