On the relative Lusternik-Schnirelmann category with respect to a closed 1-form

2009/08/10 by Tie‐Qiang Li, Tieqiang Li, Li, Tieqiang +2
Biochemistry, Genetics and Molecular Biology · Mathematics · #55M30 #55N25 #58E05 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling #math.AT #msc:55M30 #msc:55N25 #msc:58E05

paper · pdf · doi:10.48550/arxiv.0908.1294

14 pages, changed references

openalex publication_date 2009/08/10 · arxiv created 2009/11/20 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study a homotopy invariant cat(X,B,ξ) on a pair of finite CW complexes with respect to a continuous closed 1-form. This is a generalisation of a Lusternik-Schnirelmann category developed by Farber, studying the topology of a closed 1-form. The article establishes the connection with the original notion and obtains analogous results on critical points and homoclinic cycles. We also provide a similar cuplength lower bound for cat(X,B,ξ).

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