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Computational Complexity of Topological Invariants

Part of: Homotopy theory Theory of computing

Published online by Cambridge University Press:  11 December 2014

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

Keywords

computational complexitycup lengthLusternik—Schnirelmann categorypure elliptic space

MSC classification

Primary: 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
Secondary: 55P62: Rational homotopy theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 27 - 32
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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References

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