On the Lusternik-Schnirelmann category of a simplicial map

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• 作者：Nicholas A. Scoville ; ^{nscoville@ursinus.edu} ; Willie Swei ^{wiswei@ursinus.edu}
• 关键词：55M30 ; 55U05 ; 55U10 ; 06F30
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：216
• 期：Complete
• 页码：116-128
• 全文大小：340 K
• 卷排序：216

文摘

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 simplicial 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 category weight of Y. Rudyak and J. Strom.