European Journal of Mathematics

, Volume 3, Issue 2, pp 387–428 | Cite as

Algebraic and dynamical cancellations associated to spectral sequence

  • Maria A. Bertolim
  • Dahisy V. S. Lima
  • Margarida P. Mello
  • Ketty A. de RezendeEmail author
  • Mariana R. da Silveira
Research Article


We study algorithms that give rise to a global Smale’s Cancellation Theorem for dimensions \(n\geqslant 6\). The Spectral Sequence Sweeping Algorithm (SSSA) and the Row Cancellation Algorithm (RCA) for a filtered Morse chain complex on a manifold \(M^{n}\) are presented. Our main theorems, which make use of these algorithms with a connection matrix as an input, establish a correspondence between algebraic cancellations in a spectral sequence and dynamical cancellations of the gradient flow on \(M^{n}\) for dimensions \(n\geqslant 6\).


Connection matrix Morse complex Spectral sequence Integer programming 

Mathematics Subject Classification

37B30 37D15 55T05 90C10 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Maria A. Bertolim
    • 1
  • Dahisy V. S. Lima
    • 2
  • Margarida P. Mello
    • 2
  • Ketty A. de Rezende
    • 2
    Email author
  • Mariana R. da Silveira
    • 3
  1. 1.SRH Leonardo da Vinci GymnasiumNeckargemündGermany
  2. 2.IMECCUniversidade Estadual de CampinasCampinasBrazil
  3. 3.CMCCUniversidade Federal do ABCSanto AndréBrazil

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