A Morse complex for infinite dimensional manifolds - Part I

17Citations
Citations of this article
10Readers
Mendeley users who have this article in their library.

Abstract

In this paper and in the forthcoming Part II, we introduce a Morse complex for a class of functions f defined on an infinite dimensional Hilbert manifold M, possibly having critical points of infinite Morse index and co-index. The idea is to consider an infinite dimensional subbundle - or more generally an essential subbundle - of the tangent bundle of M, suitably related with the gradient flow of f. This Part I deals with the following questions about the intersection W of the unstable manifold of a critical point x and the stable manifold of another critical point y: finite dimensionality of W, possibility that different components of W have different dimension, orientability of W and coherence in the choice of an orientation, compactness of the closure of W, classification, up to topological conjugacy, of the gradient flow on the closure of W, in the case dim W = 2. © 2004 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Abbondandolo, A., & Majer, P. (2005). A Morse complex for infinite dimensional manifolds - Part I. Advances in Mathematics, 197(2), 321–410. https://doi.org/10.1016/j.aim.2004.10.007

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free