To define the Dirac-Ramond operator – which is on the loop space of a string manifold – I need to go through a rather substantial preparation which includes diferential analysis (function spaces, …

In topology, a branch of mathematics, the loop space Ω X of a pointed topological space X is the space of (based) loops in X, i.e. continuous pointed maps from the pointed circle S1 to X, equipped with the …

Loop spaces have been considered for their geometric interest (Freed Daniel 1988) where the space of based loops on a compact Lie group is endowed with a Kählerian structure; see also the survey by L …

Sep 9, 2025 · A path-connected topological space is called nilpotent, if its fundamental group is nilpotent and acts nilpotently on the higher homotopy groups.

For any based space X, let QX denote the loop space of X, i.e. the set of based maps from the circle to X, equipped with the compact open topology (see [27]). Then suspension gives rise to maps a : …

In topology, the loop space of a given space X is a new space whose "points" are the continuous loops that start and end at a fixed base point in X. Studying the structure of the loop space is fundamental …

Abstract This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as background notes to a series of seminars given at NTNU …