2003/11/11 by J. P. Pridham, Pridham, J. P. · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0311168
There has long been a philosophy that every deformation problem in characteristic zero should be governed by a differential graded Lie algebra (DGLA). In this paper, the theory of Simplicial Deformation Complexes (SDCs) is developed, as an alternative to DGLAs. These work in all characteristics, and for many problems can be constructed canonically. In particular, SDCs are constructed for the problems of deforming an arbitrary scheme, of deforming a Hopf algebra, and of deforming a representation of the fundamental group. In characteristic zero, SDCs and DGLAs are equivalent.