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cup length

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Computational Complexity of Topological Invariants
Part of
- Homotopy theory
- Theory of computing
Manuel Amann
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 1 / February 2015

Published online by Cambridge University Press:

11 December 2014, pp. 27-32
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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.