Invariants for the Smale space associated to an expanding endomorphism of a flat manifold

Invariants for the Smale space associated to an expanding endomorphism of a flat manifold
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发表时间：
2022-08
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通讯作者：
R. Chaiser;Maeve Coates-Welsh;R. Deeley;A. Farhner;Jamal Giornozi;Robi Huq;Levi Lorenzo;Jose Oyola-Cortes;Maggie Reardon;Andrew M. Stocker
R. Chaiser;Maeve Coates-Welsh;R. Deeley;A. Farhner;Jamal Giornozi;Robi Huq;Levi Lorenzo;Jose Oyola-Cortes;Maggie Reardon;Andrew M. Stocker
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作者：
R. Chaiser;Maeve Coates-Welsh;R. Deeley;A. Farhner;Jamal Giornozi;Robi Huq;Levi Lorenzo;Jose Oyola-Cortes;Maggie Reardon;Andrew M. Stocker

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.本文研究了由闭连通黎曼流形上的扩张自同态得到的Smale空间的不变量。具体地说，相关的不变量是相关的C-代数的K -理论和Smale空间的Putnam同调理论。后者同构于用于构造C-代数的广群的广群同调。
. We study invariants associated to Smale spaces obtained from an expanding endomorphism on a (closed connected Riemannian) flat mani- fold. Specifically, the relevant invariants are the K -theory of the associated C ∗ -algebras and Putnam’s homology theory for Smale spaces. The latter is isomorphic to the groupoid homology of the groupoids used to construct the C ∗ -algebras.