Operadic homology and functor homology

本课题主要研究代数拓扑和同伦代数。它研究了二面体同调和相关同调理论的方法。我们的目的是比较在文学的各种方法，并延长这些，在需要的地方，合适的无限版本的代数。所采取的方法很可能涉及从操作数和函子同源的工具。它应该给出一个概念框架，其中包含同伦不变性等属性，而不是检查公式。这些（上）同调理论的代数结构也将进行研究。

This project lies in algebraic topology and homotopical algebra. It studies approaches todihedral (co)homology and related homology theories. The aim is to compare the various approaches in the litterature and to extend these, where needed, to suitable infinity versions of algebras. The approach taken is likely to involve tools from operads and from functor homology. It should give a conceptual framework where properties such as homotopy invariance are built in rather than a matter of checking formulas. The algebraic structure of these (co)homology theories will also be investigated.