Abstract
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 \(n\geqslant 6\).
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Notes
Temporary marks are erased at the end of the iterative step.
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D.V.S.L. supported by FAPESP under Grant 2014/11943-6. K.A. de R. partially supported by CNPq under Grant 309734/2014-2 and by FAPESP under Grant 2012/18780-0. M.R. da S. partially supported by FAPESP under Grant 2012/18780-0.
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Bertolim, M.A., Lima, D.V.S., Mello, M.P. et al. Algebraic and dynamical cancellations associated to spectral sequence. European Journal of Mathematics 3, 387–428 (2017). https://doi.org/10.1007/s40879-017-0144-6
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DOI: https://doi.org/10.1007/s40879-017-0144-6