${\text{PL}}$ sheaves and their characteristic classes

Howard Osborn
1972 Bulletin of the American Mathematical Society  
Any PL manifold possesses a natural structure sheaf and a derivation into a sheaf ê of differential forms, from which one obtains the smoothable function algebra and de Rham complex of [1] via global sections. The sheaves ë are part of a fibered category of sheaves & of modules over PL structure sheaves, into which the classical category of (sheaves of local sections of) vector bundles embeds as a full subcategory. There is a Chern-Weil construction of real characteristic classes which assigns
more » ... hern classes to complex sheaves & and Euler classes to real oriented sheaves 3F in such a way that all the usual axioms are satisfied. These classes are precisely the usual real Chern and Euler classes on the subcategory of vector bundles. In this note we present definitions and statements of some of the main results concerning PL sheaves and their real characteristic classes. The details will appear in [2].
doi:10.1090/s0002-9904-1972-13036-2 fatcat:nynine6h4ve5xkgn5vflfo5fam