%0 Journal Article
%T Log differentiable spaces and manifolds with corners
%A W. D. Gillam
%A Samouil Molcho
%J Mathematics
%D 2015
%I arXiv
%X We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In the differentiable setting, our theory yields a framework for treating manifolds with corners generalizing recent work of Kottke-Melrose. We give a treatment of the theory of fans, which are to monoids as schemes are to rings. By adapting similar results from logarithmic algebraic geometry, we prove a general result on resolution of toric singularities which can be used to resolve singularities of a wide class of "log smooth" spaces.
%U http://arxiv.org/abs/1507.06752v1