2009/02/26 by Robert Waelder, Waelder, Robert
Mathematics · #14E15 #58J26 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:14E15 #msc:58J26
paper · pdf · doi:10.48550/arxiv.0902.4518
18 pages, article for MSRI Topology of Stratified Spaces Proceedings
arxiv created 2009/02/26 · arxiv updated 2009/12/01
A differential operator D commuting with an S1-action is said to be rigid if the non-constant Fourier coefficients of ker D and \coker D are the same. Somewhat surprisingly, the study of rigid differential operators turns out to be closely related to the problem of defining Chern numbers on singular varieties. This relationship comes into play when we make use of the rigidity properties of the complex elliptic genus--essentially an infinite-dimensional analogue of a Dirac operator. This paper is a survey of rigidity theorems related to the elliptic genus, and their applications to the construction "singular" Chern numbers.