Distributional category of manifolds

Ekansh Jauhari

doi:10.1007/s40590-025-00744-6

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arXiv · 2408.11036

Distributional category of manifolds

Ekansh Jauhari

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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.

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Ekansh Jauhari. 2024-08-20. Distributional category of manifolds. https://doi.org/10.1007/s40590-025-00744-6

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