Operadic homology and functor homology

本课题涉及代数拓扑和同邻代数。研究了二面体（co）同调的方法及相关的同调理论。目的是比较文献中的各种方法，并在需要时将这些方法扩展到代数的合适无穷版本。所采用的方法可能涉及来自操作数和函子同源的工具。它应该给出一个概念性框架，在这个框架中，诸如同伦不变性之类的属性是内置的，而不是检查公式的问题。这些（co）同调理论的代数结构也将被研究。

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.