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arXiv · 2606.09184

Topological complexity for closed 1-forms

Kenji Fukushi
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Abstract

Michael Farber introduced a generalization of the Lusternik--Schnirelmann category for closed 1-forms. In this paper, we introduce and study a corresponding version of topological complexity for closed 1-forms. We establish analogues of the basic properties of ordinary topological complexity, including inequalities relating this invariant to the Lusternik--Schnirelmann category for closed 1-forms. We also prove a closed 1-form analogue of the navigation-function method: upper bounds for our invariant can be obtained from the dynamical properties of gradient-like flows of closed 1-forms.

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Kenji Fukushi. 2026-06-08. Topological complexity for closed 1-forms. https://arxiv.org/abs/2606.09184

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