Department of Mathematics, National Tsing Hua University

參考連結
https://sites.google.com/view/sgsnthu/home

Abstract:
In his study of Rozansky–Witten invariants, Kapranov discovered a natural $L_infty[1]$-algebra structure on the Dolbeault complex $Omega^{0, bullet}(T_X^{1, 0})$ of an arbitrary Kähler manifold $X$, where all multibrackets are $Omega^{0, bullet}(X)$-multilinear except for the unary bracket. Motivated by this example, we introduce an abstract notion of Kapranov L-infinity algebras, and prove  that associated to any dg Lie algebroid, there is a natural Kapranov L-infinity algebra. We also discuss the linearization problem. This is a  joint work with Ruggero Bandiera, Seokbong Seol, and Mathieu Stiénon.