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On the space of trajectories of a generic gradient like vector field


Burghelea, D; Friedlander, L; Kappeler, T (2010). On the space of trajectories of a generic gradient like vector field. Analele. Universităţii de Vest din Timişoara. Seria Matematicǎ-Informaticǎ, 48(1-2):45-126.

Abstract

In this paper the authors explain, in great detail, how to equip the compactified (un)stable sets and trajectory spaces of a gradient-like vector field with the structure of a smooth manifold with corners, in a canonical way. This is done for vector fields which are gradient-like with respect to a proper Morse function, satisfy the Smale transversality condition, and are of standard form, ∑i≤qxi∂∂xi−∑i>qxi∂∂xi, near the zeros (critical points). As an application, the authors discuss the integration homomorphism relating the de Rham complex and the Thom–Smale complex with coefficients in a representation of the fundamental group.

Abstract

In this paper the authors explain, in great detail, how to equip the compactified (un)stable sets and trajectory spaces of a gradient-like vector field with the structure of a smooth manifold with corners, in a canonical way. This is done for vector fields which are gradient-like with respect to a proper Morse function, satisfy the Smale transversality condition, and are of standard form, ∑i≤qxi∂∂xi−∑i>qxi∂∂xi, near the zeros (critical points). As an application, the authors discuss the integration homomorphism relating the de Rham complex and the Thom–Smale complex with coefficients in a representation of the fundamental group.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2010
Deposited On:11 Apr 2013 13:41
Last Modified:07 Dec 2017 18:16
Publisher:Univ. Vest Timişoara
ISSN:1841-3293
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.ams.org/mathscinet-getitem?mr=2849328

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