2016/07/26 by Grigory Papayanov, Papayanov, Grigory
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.1607.07509
10 pages
arxiv created 2016/07/26 · arxiv updated 2016/07/27
In \citeGoto, Ryushi Goto has constructed the deformation space for a manifold equipped with a collection of closed differential forms and showed that in some important cases (Calabi-Yau, G2- and Spin(7)-structures) this deformation space is smooth. This result unifies the classical Bogomolov-Tian-Todorov and Joyce theorems about unobstructedness of deformations. Using the work of Fiorenza and Manetti, we show that this deformation space could be obtained as the deformation space associated to a certain L∞-algebra. We also show that for Calabi-Yau, G2- and Spin(7)-structures this L∞-algebra is homotopy abelian. This gives a new proof of Goto's theorem.