Cyclic and simplicial cohomology of Banach algebras

Banach 代数的循环和单纯上同调

• 批准号: 184058-2012
• 负责人: Gourdeau, Frédéric
• 金额: $ 0.87万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569693
• 关键词: Cyclic; simplicial; cohomology; Banach; algebras

When looking at an everyday object, like a cup, one can count the holes in the object. For some mathematical work, the precise shape of the object one is considering does not matter too much: what matters is how many holes it has. These holes vary in nature: in a cup, the hole in the handle is different from the hole you pour coffee in. You can imagine flattening a cup if it was made of some stretchable material, but without gluing or cutting, the whole in the handle will always remain visible. Mathematical tools have been developed to deal with such concepts: they are varied and apply not only to objects similar to a cup but also to spaces. In our research, we look at spaces of functions and at characteristics of these spaces. For a mathematician, this is a meeting place for algebra and analysis. It is fundamental research, rich, intriguing and varied.

当观察一个日常物体（例如杯子）时，人们可以数出物体上的孔。对于某些数学工作，所考虑的物体的精确形状并不重要：重要的是它有多少个孔。这些孔的性质各不相同：在杯子中，手柄上的孔与倒咖啡的孔不同。您可以想象如果杯子是由某种可拉伸材料制成的，则将其压平，但如果不使用胶合或切割，手柄中的整体将始终保持可见。 人们开发了数学工具来处理这些概念：它们多种多样，不仅适用于类似于杯子的物体，也适用于空间。在我们的研究中，我们着眼于功能空间以及这些空间的特征。对于数学家来说，这是代数和分析的聚会场所。它是基础研究，内容丰富、有趣且多样。