论文标题
动力学系统的同源性和K理论III。超越稳定断开的蓝色空间
Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces
论文作者
论文摘要
我们研究了由Smale空间引起的典型群体类型的同种异体不变，继续我们以前的工作，但通过将分辨率纳入空间方向而超越了稳定的断开案例。我们表明，Putnam定义的同源组与具有整数系数的Crainic-Moerdijk群体同源物是同构。我们还表明，稳定和不稳定的等效关系的C*代数的K组具有有限的等级。对于不稳定的断开的Smale空间，我们提供了一个共同的光谱序列，其第二页是（稳定）同源组，并收敛到不稳定的C*-Algebra的K组。
We study homological invariants of étale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology groups defined by Putnam are isomorphic to the Crainic-Moerdijk groupoid homology with integer coefficients. We also show that the K-groups of C*-algebras of stable and unstable equivalence relations have finite rank. For unstably disconnected Smale spaces, we provide a cohomological spectral sequence whose second page is the (stable) homology groups, and converges to the K-groups of the unstable C*-algebra.
