22 citations · 53 across the 13 of their papers we have counts for
8 papers · 1 filter
Yet More Smooth Mapping Spaces and Their Smoothly Local Properties
Andrew Stacey
Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to…
The co-Riemannian Structure of Smooth Loop Spaces
Andrew Stacey
We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a string manifold is a per-Hilbert-Sc…
How to Construct a Dirac Operator in Infinite Dimensions
Andrew Stacey
We define the notion of a co-Riemannian structure and show how it can be used to define the Dirac operator on an appropriate infinite dimensional manifold. In particular, this appr…
The Smooth Structure of the Space of Piecewise-Smooth Loops
Andrew Stacey
We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a par…
Comparative Smootheology
Andrew Stacey
We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Frölicher, Sikorski, Smith, and Souriau. The method of compa…
Constructing Smooth Loop Spaces
Andrew Stacey
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard c…