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A Computational Framework for the Connection Matrix Theory. (arXiv:1810.04552v1 [math.AT])
来源于:arXiv
The connection matrix is a powerful algebraic topological tool from Conley
index theory that captures relationships between isolated invariant sets.
Conley index theory is a topological generalization of Morse theory in which
the connection matrix subsumes the role of the Morse boundary operator. Over
the last few decades, the ideas of Conley have been cast into a purely
computational form. In this paper we introduce a computational, categorical
framework for the connection matrix theory. This contribution transforms the
computational Conley theory into a computational homological theory for
dynamical systems. More specifically, within this paper we have two goals: 1)
We cast the connection matrix theory into appropriate categorical,
homotopy-theoretic language. We identify objects of the appropriate categories
which correspond to connection matrices and may be computed within the
computational Conley theory paradigm by using the technique of reductions. 2)
We describe an algorithm for 查看全文>>