论文标题
合理同态理论中的形式和有限性
Formality and finiteness in rational homotopy theory
论文作者
论文摘要
我们在空间上分段多项式形式的沙利文代数的差分级代数模型中探索各种形式和有限性。可以根据其基本组的Malcev Legebra的过滤和分级形式性能重新解释该空间的1个义务属性，而该空间的某些有限属性则反映在与之相关的代数模型的有限属性中。反过来，代数模型的形式性和有限性能对该空间的共同体跳跃基因座的几何形状具有很强的影响。我们以从复杂的代数几何形状，紧凑的谎言群和3维流形的示例来说明了理论。
We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms of the filtered and graded formality properties of the Malcev Lie algebra of its fundamental group, while some of the finiteness properties of the space are mirrored in the finiteness properties of algebraic models associated with it. In turn, the formality and finiteness properties of algebraic models have strong implications on the geometry of the cohomology jump loci of the space. We illustrate the theory with examples drawn from complex algebraic geometry, actions of compact Lie groups, and 3-dimensional manifolds.
