A geometric description of differential cohomology
A geometric description of differential cohomology
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微分上同调的几何描述
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
T. Schick
中科院分区：
文献类型：
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作者：
U. Bunke;M. Kreck;T. Schick
本文给出了双曲积分上同调的几何配边刻画。考虑该模型的主要动机（其他模型见[5，6，7，8]）是它允许对杯产品和集成进行简单描述。特别是，很容易验证这些结构的相容性。我们在[4]中构造的双曲配边的情况下以类似的方式进行。在那里的出发点是奎伦的cobordism描述奇异cobordism群的diestenchmanifold X。在这里，我们使用类似的描述积分上同调从[11]。这个上同调理论用SH（X）表示。在这种描述中，奎伦描述中的光滑流形被所谓的层状空间（stratifolds）所取代。上同调理论SH（X）与普通积分上同调H（X）自然同构，从而得到普通积分上同调的双曲扩张的一个配边型定义。
In this paper we give a geometric cobordism description of dierential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of dierential cobordism as constructed in [4]. There the starting point was Quillen’s cobordism description of singular cobordism groups for a dierential manifold X. Here we use instead the similar description of integral cohomology from [11]. This cohomology theory is denoted by SH (X). In this description smooth manifolds in Quillen’s description are replaced by so-called stratifolds, which are certain stratified spaces. The cohomology theory SH (X) is naturally isomorphic to ordinary integral cohomology H (X), thus we obtain a cobordism type definition of the dierential extension of ordinary integral cohomology.
Landweber 精确的形式群定律和平滑上同调理论
DOI：
10.2140/agt.2009.9.1751
发表时间：
2009
期刊：
arXiv: K-Theory and Homology
影响因子：
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作者：
U. Bunke;T. Schick;I. Schröder;M. Wiethaup
通讯作者：
M. Wiethaup