AI 中文总结
研究定义弱汇编器的霍赫希尔德同调，构造从其群完备K-理论到霍赫希尔德同调的丹尼斯迹映射，计算相关同调，给出0级映射描述，还表明丹尼斯迹是对博曼等人定义映射的细化，证明群同调是迹不变量。
AI 中文摘要
我们定义了弱汇编器的霍赫希尔德同调的概念，并利用它构造了一个从弱汇编器的群完备K-理论到其霍赫希尔德同调的丹尼斯迹映射。我们计算了一些例子的霍赫希尔德同调，特别是受限多面体的各种情况。我们还给出了0级丹尼斯迹映射的明确描述。此外，我们表明丹尼斯迹是博曼等人定义的迹/调节器映射的细化，从而表明群同调是迹不变量。
英文摘要
We define a notion of Hochschild homology of a weak assembler and use it to construct a Dennis trace map from the group completion $K$-theory of a weak assembler to its Hochschild homology. We compute the Hochschild homology for some examples, in particular for various cases of restricted polytopes. We also give an explicit description of the Dennis trace map at level $0$, i.e. from the zeroth $K$-theory group to the zeroth Hochschild homology group. Further, we show that the Dennis trace is a refinement of the trace/regulator map defined by Bohmann et al thus showing that group homology is a trace invariant.
Comments39 pages, comments welcome
