The concept of orbifolds should unify differential geometry with equivariant homotopy theory,
so that orbifold cohomology should unify differential cohomology with proper equivariant …

Many important theorems in differential topology relate properties of manifolds to properties
of their underlying homotopy types--defined eg using the total singular complex or the\v {C} …

It is well known that any model for derived manifolds must form a higher category. In this
paper, we propose a universal property for this higher category, classifying it up to …

We describe various equivalent ways of associating to an orbifold, or more generally a
higher étale differentiable stack, a weak homotopy type. Some of these ways extend to …

In this note we endow the∞-topos Diff r of sheaves on the category of Cr-manifolds with the
structure of a fractured∞-topos and use this structure to give a simple proof that closed …

A new approach to\'etale homotopy theory is presented which applies to a much broader
class of objects than previously existing approaches, namely it applies not only to all …

For a log scheme locally of finite type over ℂ, a natural candidate for its profinite homotopy
type is the profinite completion of its Kato–Nakayama space. Alternatively, one may consider …

We give a complete and categorical characterization of étale stacks (generalized orbifolds)
in various geometric contexts, including differentiable stacks and topological stacks. This …

Motivated by D. Roytenberg's observation in\cite {roytenberg4} that Leibniz algebras can be
regarded as a kind of weak Lie 2-algebra, and the results of M. Kinyon\cite {kinyon} and S …

A well-known principle in the theory of Lie groupoids asserts that the tranverse geometry of a
Lie groupoid models the geometry of the associated differentiable stack. This statement …