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.

当看着像杯子这样的日常物品时，人们可以数一数物体上的洞。对于一些数学工作来说，人们正在考虑的物体的精确形状并不太重要：重要的是它有多少个洞。这些洞的性质各不相同：在杯子中，手柄上的洞与你倒入咖啡的洞不同。你可以想象一下，如果杯子是由一些可伸缩的材料制成的，那么它就会变平，但如果没有粘合或切割，手柄上的整个杯子将始终可见。 已经开发出数学工具来处理这样的概念：它们是多种多样的，不仅适用于类似杯子的物体，也适用于空间。在我们的研究中，我们着眼于函数空间以及这些空间的特征。对于数学家来说，这里是代数和分析的聚集地。这是一项基础性研究，内容丰富、耐人寻味、种类繁多。