Applied Topology

该研究项目的主要目标是推动应用拓扑学在几个方面的主题，提供一个重大的进步作为一个整体的结果。我们建议在两个主要方向上开展工作：组合挠和回避，以及并发拓扑。在第一个方向，我们计划通过使用一种新的策略来接近该领域的一个主要猜想，从而加强组合代数拓扑的理论基础。在第二个方向，我们希望把现有的并发性和理论上的分布式计算的发展结合起来，从而发展我们所说的知识拓扑。此外，在这里有一些明确的aesturtures，我们计划攻击。整个项目充满了思想的定量拓扑，其中实际单纯细分获得特别重要的。

The main objective of this research project is to drive forward the subject of Applied Topology on several fronts, providing a major advancement as a total result. We propose to work in 2 main directions: combinatorial torsions and evasiveness, and topology in concurrency.In the first direction, we plan to strengthen the theoretical foundations of combinatorial alge- braic topology by using a novel strategy to approach a major conjecture in the field.In the second direction, we want to bring together the existing developments on concurrency and theoretical distributed computing and thus develop what we call the topology of knowl- edge. Also here there is a number of explicit conjectures which we plan to attack.The whole project is suffused with ideas of quantitative topology, where the actual simplicial subdivision gains special importance.