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Computational Complexity of Topological Invariants

Published online by Cambridge University Press:  11 December 2014

Manuel Amann*
Affiliation:
Department of Mathematics, University of Toronto, Earth Sciences 2146, Toronto, ON M5S 2E4, Canada

Abstract

We answer the following question posed by Lechuga: given a simply connected space X with both H* (X; ℚ) and π*(X) ⊗ ℚ being finite dimensional, what is the computational complexity of an algorithm computing the cup length and the rational Lusternik—Schnirelmann category of X?

Basically, by a reduction from the decision problem of whether a given graph is k-colourable for k ≥ 3, we show that even stricter versions of the problems above are NP-hard.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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References

1.Anick, D. J., The computation of rational homotopy groups is #P-hard, in Computers in geometry and topology, Lecture Notes in Pure and Applied Mathematics, Volume 114, pp. 156 (Dekker, New York, 1989).Google Scholar
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