Distributional category of manifolds

Abstract

Recently, a new homotopy invariant of metric spaces, called the distributional LS-category, was defined, which provides a lower bound to the classical LS-category. In this paper, we obtain several sufficient conditions for the distributional LS-category (dcat) of a closed manifold to be maximum, i.e., equal to its classical LS-category (cat). These give us many new computations of dcat, especially for some essential manifolds and (generalized) connected sums. In the process, we also determine the cat of closed 3-manifolds having torsion-free fundamental groups and some closed geometrically decomposable 4-manifolds. Finally, we extend some of our results to closed Alexandrov spaces with curvature bounded below and discuss their cat and dcat in dimension 3.

arXiv commentTitle changed, introduction rewritten, and some other changes made based on the referee report. 31 pages

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Cited by in corpus (2)

• Bochner-type theorems for distributional category
• LS-category and sequential topological complexity of symmetric products