arXiv subjects

Kenji Fukushi

Publications and source records attributed to Kenji Fukushi.

2 recordsLinked to original sources

arXiv2026

Lusternik-Schnirelmann category of Lee Forms on locally conformally symplectic manifolds

The Lusternik--Schnirelmann category of a closed symplectic manifold admits various estimates. Locally conformally symplectic (LCS) geometry is a generalization of symplectic geometry involving a closed one-form, called the Lee form. In this paper, we introduce Farber's Lusternik--Schnirelmann category for closed one-forms into LCS geometry by applying it to the Lee class. In particular, this provides a new topological approach to LCS structures of the second kind. We then obtain lower bounds for this invariant under LCS blow-ups.

math.SG↗

arXiv2026

Topological complexity for closed 1-forms

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.

math.AT↗