Evaluation of the Transfer and the Universal Surgery Classes.
Let be a ring. In two previous articles [12, 14] we studied the homotopy category of projective -modules. We produced a set of generators for this category, proved that the category is -compactly generated for any ring , and showed that it need not always be compactly generated, but is for sufficiently nice . We furthermore analyzed the inclusion and the orthogonal subcategory . And we even showed that the inclusion has a right adjoint; this forces some natural map to be an equivalence...
Let Sr be the category of r-reduced simplicial sets, r ≥ 3; let Lr-1 be the category of (r-1)-reduced differential graded Lie algebras over Z. According to the fundamental work [3] of W.G. Dwyer both categories are endowed with closed model category structures such that the associated tame homotopy category of Sr is equivalent to the associated homotopy category of Lr-1. Here we embark on a study of this equivalence and its implications. In particular, we show how to compute homology, cohomology,...
The purpose of this note is to prove the exponential law for uniformly continuous proper maps.