The exponential map on the free loop space is Fredholm
type: Item
instance of: scholarly article
title: The exponential map on the free loop space is Fredholm
zbMATH Open document ID: 0906.58002
published in: Geometric and Functional Analysis. GAFA
publication date: 1999-01-31T00:00:00Z
review text: In the main result of the paper, sufficient conditions for the exponential map of an infinite-dimensional Riemannian (Hilbert) manifold to be a nonlinear Fredholm map of index zero are given. This result can be applied to the free loop space of a finite-dimensional manifold. In particular, it follows that for a conjugate point the derivative of the exponential map is neither injective nor surjective which answers a question posed by W. Klingenberg. Another consequence is that conjugate points on the free loop space cannot cluster along finite geodesic arcs.
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 1123716
zbMATH Keywords: exponential map
zbMATH Keywords: free loop space
zbMATH Keywords: conjugate points
zbMATH Keywords: Hilbert (Riemannian) manifolds
author: Gerard Misiołek
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
full work available at URL: s000390050032
OpenAlex ID: W2305617506
DOI: 10.1007/S000390050032
description: scientific article; zbMATH DE number 1123716