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Type: Artigo de periódico
Title: Conley's spectral sequence via the sweeping algorithm
Author: de Rezende, KA
Mello, MP
da Silveira, MR
Abstract: In this article we consider a spectral sequence (E(r), d(r)) associated to a filtered Morse-Conley chain complex (C, Delta), where Delta is a connection matrix. The underlying motivation is to understand connection matrices under continuation. We show how the spectral sequence is completely determined by a family of connection matrices. This family is obtained by a sweeping algorithm for Delta over fields IF as well as over Z. This algorithm constructs a sequence of similar matrices Delta(0) = Delta, Delta(1), ... , where each matrix is related to the others via a change-of-basis matrix. Each matrix Delta(r) over F (resp., over Z) determines the vector space (resp., Z-module) E(r) and the differential dr. We also prove the integrality of the final matrix Delta(R) produced by the sweeping algorithm over Z which is quite surprising, mainly because the intermediate matrices in the process may not have this property. Several other properties of the change-of-basis matrices as well as the intermediate matrices Delta(r) are obtained. (C) 2010 Elsevier By. All rights reserved.
Subject: Connection matrix
Spectral sequences
Sweeping algorithm
Conley index
Integer programming
Country: Holanda
Editor: Elsevier Science Bv
Citation: Topology And Its Applications. Elsevier Science Bv, v. 157, n. 13, n. 2111, n. 2130, 2010.
Rights: fechado
Identifier DOI: 10.1016/j.topol.2010.05.008
Date Issue: 2010
Appears in Collections:Unicamp - Artigos e Outros Documentos

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