The rational [bold]PL de Rham theory of Sullivan is developed and generalized, using methods of Quillen's "homotopical algebra." For a field k of characteristic 0, a pair of contravariant adjoint functors A : (Simplicial sets) [right arrow over left arrow] (Commutative DG k-alge…
Classifying spaces in surgery theory were first used by Sullivan and Casson in their (independent) unpublished work on the Hauptvermutung for PL manifolds. In his 1968 Ph.D. thesis, F. Quinn developed a general theory of surgery classifying spaces, realizing the Wall surgery gro…
This text discusses the Euler class, the intersection number, the Lefschetz number, and the Thom class. The aim of discussing these well-known concepts is to describe them in a "computable" way. These will be expressed in differential or integral forms, giving formulae, generali…