PROP profile of deformation quantization and graph complexes with loops and wheels

拟李双代数与伪李双代数的（带轮）properad的图复形与形变理论

Graph complexes and Deformation theories of the (wheeled) properads of quasi- and pseudo-Lie bialgebras

本文研究强同伦拟李双代数的导子复形（含无轮、带轮情形），并借助Kontsevich图复形计算其上同调，推进拟李双代数相关形变理论研究。

强同伦李双代数轮式 properad 的形变理论与图复形

Deformation theory of the wheeled properad of strongly homotopy Lie bialgebras and graph complexes

本文研究强同伦李双代数轮式 properad 及其次数平移版本的导子复形，证明其与 Kontsevich 图复形拟同构，并得出同伦非平凡导子李代数为两个 $\mathfrak{grt}$ 副本直和的结论。

Permutahedra, HKR isomorphism and polydifferential Gerstenhaber-Schack complex

This paper aims to give a short but self-contained introduction into the theory of (wheeled) props, properads, dioperads and operads, and illustrate some of its key ideas in terms of a prop(erad)ic interpretation of simplicial and permutahedra cell complexes with subsequent applications to the Hochschild-Kostant-Rosenberg type isomorphisms.

Wheeled props in algebra, geometry and quantization

These are expanded notes of author's talk at the ECM 2008 attempting to give an elementary introduction into the main ideas of the theory of wheeled props for beginners, and also a survey of its most recent major applications (ranging from algebra and geometry to deformation theory and Batalin-Vilkovisky quantization) which might be of interest to experts.

From deformation theory of wheeled props to classification of Kontsevich formality maps

We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teichmueller group acts on that wheeled prop faithfully and homotopy non-trivially. Next we apply this homotopy theory to the study of the deformation complex of an arbitrary Maxim Kontsevich formality map and compute the full cohomology group of that deformation complex in terms of the cohomology of a certain graph complex introduced earlier by Maxim Kontsevich in [K1] and studied by Thomas Willwacher in [W1].

控制 props 与 wheeled props 的 Koszul operads

Koszul Operads Governing Props and Wheeled Props

本文构造了控制 props 和 wheeled props 的群胚着色 operads，证明其 Koszul 性，并由此定义同伦 props、构造 Massey 积以刻画形变性，重获 Mac Lane 定理。