On the Lusternik-Schnirelmann category of a simplicial map

Nicholas A. Scoville; Willie Swei

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arXiv · 1606.01205

On the Lusternik-Schnirelmann category of a simplicial map

Nicholas A. Scoville·Willie Swei

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Abstract

In this paper, we study the Lusternik-Schnirelmann category of a simplicial map between simplicial complexes, generalizing the simplicial category of a complex to that of a map. Several properties of this new invariant are shown, including its relevance to products and fibrations. We relate this category of a map to the classical Lusternik-Schnirelmann category of a map between finite topological spaces. Finally, we show how the simplicial category of a map may be used to define and study a simplicial version of the essential category weight of J. Strom.

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BibTeX RIS

Nicholas A. Scoville, Willie Swei. 2016-06-03. On the Lusternik-Schnirelmann category of a simplicial map. https://arxiv.org/abs/1606.01205

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